In Exercises 9–42, find the area of the indicated region. We suggest that you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answers.
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Applied Calculus
- Find the value of c > 0 such that the regionbounded by the cubic y = x(x - c)2 and the x-axis on the interval[0, c] has area 1.arrow_forwardIn the given equation find a such that the line x a divides the region bounded by the graphs of the equations into two regions of equal area y = x, y =4, x = 0arrow_forwardFind c > 0 c > 0 such that the area of the region enclosed by the parabolas y = x 2 − c 2 y = x 2 - c 2 and y = c 2 − x 2 y = c 2 - x 2 is 100 100 .arrow_forward
- Let R be the region in R 2 bounded by the x-axis, the parabola y = x 2 and the line x = 2arrow_forwardThe base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The cross-sections perpendicular to the x-axisare rectangles of perimeter 20.arrow_forwardIn Exercises 36–38, find the point on the given curve closest tothe specified point. Recall that if you minimize the square ofthe distance, you have minimized the distance as well. 36. (1, 1) and √x +√y = 237. (0, 0) and xn + yn = 1 for n a positive, odd integer38. (0, 0) and xn + yn = 1 where n > 2 is a positive, evenintegerarrow_forward
- In his work Nova stereometria doliorum vinariorum (New Solid Geometry of a Wine Barrel), published in 1615, astronomer Johannes Kepler stated and solved the following problem: Find the dimensions of the cylinder of largest volume that can be inscribed in a sphere of radius R. Hint: Show that an inscribed cylinder has volume 2πx(R2 − x2), where x is one-half the height of the cylinder.arrow_forwardSketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.arrow_forwardFind the value of c such that the regionbounded by y = c sin x and the x-axis on the interval [0, ∏] hasarea 1.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage