In Problems 21–26, use the description of the region R to evaluate the indicated
23.
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- 5. Evaluate the integral of 1 y¹/³ (x³ + 1) over the region which is bounded by the x axis, the line x = -y¹/3 and the line x = 3. f(x, y) =arrow_forward10. The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*f(x) dx + [° g(x) dx, where aarrow_forwardQuestion 8. Use a change of variable to compute the integral 10 R x+ y where R is the triangular region bounded by the line x + y = -1 and the coordinate axes.arrow_forward3. Use the graph and the actual areas of the indicated regions to evaluate the integrals in the following problems. a. b. C. d f(x) dx = f(x) [*1x) dx = 5 'b d f(x) dx = f(x) A a B b с \y = f(x) Area A = 1 Area B = 2 Area C = 2 →x Area D = 0.6arrow_forward5. Find the area of the region. (a) y = sinx, y = x, x = π/2, x = π (b)x= 1-y², x = y² - 1 (c) 4x + y² = 12, x = yarrow_forward4. Write both the integrals from Green's theorm for F = and y = 0 for 0 ≤ x ≤ T. (3y, 4x) with the region R bounded by y = sin aarrow_forward15. Use the indicated change of variables to evaluate the double integral ||18xy ||18xy dA where R is the rectangle with vertices (0,1),(1,2),(2,1),(1,0) R 1 X = 2 1 y =- (u +v) 2arrow_forwardQuestion 1. Use a change of variables to compute the integral /I. rydxdy, x3, y = 2x3, x = y³ and where R is the region in the first quarter bounded by the curves y = x = 2y3.arrow_forwardCTION 5.e • Evaluate the integral ſf * ds, where f (x,y) = yсos(2лx) and the value of "C" is represented by a triangle with the following vertices: (0,1), (1,0), (0,0)arrow_forward33. The graph of f is shown. Evaluate each integral by inter- preting it in terms of areas. (a) ff(x) dx (c) ff(x) dx yk 2 0 2 (b) f(x) dx (d) ff(x) dx y=f(x) 4 6 X² 8 xarrow_forward2. Evaluate each of the following line integrals in two ways*. F (x, y) = (2x – cos y) i+ (x sin y) and C1 is the straight-line path from (-4,0) to (0,5). (a) | F dr, where C1 F-(x, y) = (2x – y) i + (2x + y) j and C2 is a circle of radius 4 centered at the origin, traversed once counterclockwise starting at (4,0). (b) / F2· dĩ, where F2 · dr, where C2 Acceptable ways to evaluate the integral: * • Directly: Parametrize the path and write the integral in terms of your parametrization. • Using the Fundamental Theorem of Line Integrals: Write the theorem and show what you substitute for each part. • Using Green's Theorem: Write the theorem and show what you substitute for each part.arrow_forward22. Evaluate the iterated integral. (b) f. [, 2x + »)'dy (a) x+y+ xy dydxarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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