15. Q15
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Similar Question 1
<p>Find the area of the region bounded by the curves <code class='latex inline'>y=x+2</code> and <code class='latex inline'>y=x^2</code>.</p>
Similar Question 2
<p> Find the area of the shaded region.</p><img src="/qimages/2455" />
Similar Question 3
<p>Find the area of the shaded region.</p><img src="/qimages/5365" />
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Find the area of the region bounded by the parabola <code class='latex inline'>y = x^2</code>, the tangent line to this parabola at <code class='latex inline'>(1, 1)</code>, and the x-axis.</p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y = \sec^2x, y = 8\cos x, -\frac{\pi}{3}\leq x \leq \frac{\pi}{3} </code></p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle 4x + y^2 =12, x = y </code></p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle x = 1 - y^2, x = y^2 -1 </code></p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle y =\sin x, y=2x/\pi, x\geq 0 </code></p>
<p>Find the area of the region bounded by the curves <code class='latex inline'>y=x+2</code> and <code class='latex inline'>y=x^2</code>.</p>
<p> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'> \displaystyle y = x + 1, y = (x - 1)^2, x = -1, x = 2 </code></p>
<p>Use calculus to find the area of the triangle with the given vertices.</p><p><code class='latex inline'>\displaystyle (2, 0), (0, 2), (-1, 1) </code></p>
<p>Evaluate the integral and interpret it as the area of a region. Sketch the region.</p><p><code class='latex inline'>\displaystyle \int^{\pi/2}_{0} |\sin x -\cos 2x|dx </code></p>
<p> Find the area of the shaded region.</p><img src="/qimages/2454" />
<p> Find the area of the shaded region.</p><img src="/qimages/2453" />
<p> Evaluate the integral and interpret it as the area of a region. Sketch the region.</p><p><code class='latex inline'> \displaystyle \int^{\pi}_{0} |\sin x - \frac{2}{\pi}x|dx </code></p>
<p> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'> \displaystyle y = |x|, y = x^2 - 2 </code></p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle y = (x-2)^2, y = x </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle x = y^4, y = \sqrt{2- x}, y = 0 </code></p>
<p>Find the area of the shaded region.</p><img src="/qimages/5364" />
<p>Find the area of the shaded region.</p><img src="/qimages/5366" />
<p> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'> \displaystyle y = \cos x, y = \sin 2x , x = 0, x = \pi/2 </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y= \sqrt{x-1}, x - y =1 </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y =\sqrt[3]{2x}, y =\frac{1}{8}x^2, 0 \leq x \leq 6 </code></p>
<p>Find the area of the region bounded by the curves <code class='latex inline'>y=-x</code> and <code class='latex inline'>y=x-x^2</code>.</p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y =x^2, y = 4x -x^2 </code></p>
<p>Find the number <code class='latex inline'>a</code> such that the line <code class='latex inline'>x = a</code> bisects the area under the curve <code class='latex inline'>y=\frac{1}{x^2}, 1\leq x \leq 4</code>.</p>
<p>Find the number <code class='latex inline'>b</code> such that the line <code class='latex inline'>y = b</code> divides the region bounded by the curves <code class='latex inline'>y =x^2</code> and <code class='latex inline'>y =4</code> into two regions with equal area.</p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y = 12-x^2, y=x^2 -6 </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y = x^3, y=x </code></p>
<p> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'> \displaystyle y = 1 + \sqrt{x}, y = (3 + x)/3 </code></p>
<p>a) Find the number <code class='latex inline'>a</code> such that the line <code class='latex inline'>x = a</code> bisects the area under the curve <code class='latex inline'>y=\frac{1}{x^2}, 1\leq x \leq 4</code>.</p><p><strong>just do this one</strong> b) Find the number <code class='latex inline'>b</code> such that the line <code class='latex inline'>y = b</code> bisects the area in part (a).</p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y = \frac{1}{4}x, y = 2x^2, x + y = 3, x\geq 0 </code></p>
<p>Evaluate the integral and interpret it as the area of a region. Sketch the region.</p><p><code class='latex inline'> \displaystyle \int^{1}_{-1}|3^x -2^x|dx </code></p>
<p>Find the area of the shaded region.</p><img src="/qimages/5367" />
<p>Use calculus to find the area of the triangle with the given vertices.</p><p><code class='latex inline'>\displaystyle (0, 0), (3, 1), (1, 2) </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y = \tan x, y =2\sin x, -\frac{\pi}{3} \leq x \leq \frac{\pi}{3} </code></p>
<p>Find the area of the region enclosed between the curves <code class='latex inline'>y=1+2x</code> and <code class='latex inline'>y=1+x+\sqrt{2x}</code>.</p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle y =e^x, y = x^-1, x = -1, x =1 </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y =\cos x, y = 2-\cos x, 0 \leq x \leq 2\pi </code></p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle y = \sin x, y =x, x =\frac{\pi}{2}, x = \pi </code></p>
<p> Find the area of the shaded region.</p><img src="/qimages/2456" />
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y =\cos \pi x, y = 4x^2 -1 </code></p>
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle y = x^2 -4x, y =2x </code></p>
<p>Find the values of <code class='latex inline'>c</code> such that the area of the region bounded by the parabolas <code class='latex inline'>y=x^2-c^2</code> and <code class='latex inline'>y =c^2-x^2</code> is 576.</p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y =\cos x, y = 1-\cos x, 0 \leq x \leq \pi </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle x=2y^2, x =4 + y^2 </code></p>
<p> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'> \displaystyle y = x, y = x^2 </code></p>
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y =x^4, y = 2-|x| </code></p>
<p>The graphs of two functions are shown with the areas of the regions between the curves indicated.</p><p>a) What is the total area between the curves for <code class='latex inline'>0\leq x \leq 5</code> ?</p><p>b) What is the value of <code class='latex inline'> \int^{5}_{0}[f(x) -g(x)]dx</code>?</p><img src="/qimages/5368" />
<p>Sketch the region enclosed by the given curves and find its area.</p><p><code class='latex inline'>\displaystyle y = \frac{1}{x}, y = x, y =\frac{1}{4}x, x > 0 </code></p>
<p> Evaluate the integral and interpret it as the area of a region. Sketch the region.</p><p><code class='latex inline'> \displaystyle \int^{1}_{-1} |x^3 - x|dx </code></p>
<p> Find the area of the shaded region.</p><img src="/qimages/2455" />
<p>Sketch the region enclosed by the given curves. Decide whether the integrate with respect to <code class='latex inline'>x</code> or <code class='latex inline'>y</code>. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.</p><p><code class='latex inline'>\displaystyle y = 1/x, y = 1/x^2, x = 2 </code></p>
<p>Find the area of the shaded region.</p><img src="/qimages/5365" />
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