Please solve this

Determine the indefinite integral. Check your work by differentiation. Solve the problem. 3) Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 32 cos 5t, v(0) = 2, s(0) = 4 Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed. 4) f(x) =9- x2 between x = -3 and x = 3 using the left and right sum with n=3 rectangles of equal width. Graph the integrand and use geometry to evaluate the integral. 5 ) J V49 - x 2 dx Find the point(s) at which the given function equals its average value on the given interval. 6) f ( x ) = 2 - x2; [-6, 3] Evaluate the integral. 7) [ In x6 * dx x Use the substitution formula to evaluate the integral. dx V81 - x 2 -3TC/2 sin 0 de 10) 2 + cos 0