The figure to the right shows four regions bounded by the graph of y=xsin x: R₁, R2, R3, and R4, whose areas are 1, л-1, +1, and 2л-1, respectively. Use this information to evaluate the following integral. Π S 0 x sin x dx 元 Sxsin x x sin x dx = 0 (Type an exact answer, using as needed.) 2 Area = 1 y=xsin x Area = +1 R₁ R₂ 플 2 R3 -2 Area = -1 Area 2-1 The figure to the right shows the area of regions bounded by the graph of f and the x-axis. Evaluate the following integral. с Sf(x)dx a C froxjdx=(Type an integer or a simplified fraction.) a 24 y = f(x) 5 13 The figure to the right shows the area of regions bounded by the graph of f and the x-axis. Evaluate the following integral. 0 f(x)dx So 0 f(x)dx = (Type an integer or a simplified fraction.) 14 y = f(x) 4 12 Use geometry (not Riemann sums) to evaluate the following definite integral. 5 So f 5 if x ≤4 0 f(x)dx where f(x)=2x-3 if x>4 The following function is positive and negative on the given interval. π f(x) = sin 3x; a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4. Π c. Use the sketch in part (a) to show which intervals of л make positive and negative contributions to the net area. 2