Calculate the integral of f(x) = sin(x) from x = 0 to x = π/2.

Graph the polynomial function \( f(x)=(x+1)^{2}(x-6)^{2} \) using parts (a) through (e). The graph of \( f \) behaves like \( y=x^{4} \) for large values of \( |x| \). (b) Find the \( x \) - and \( y \)-intercepts of the graph of the function. The \( x \)-intercept(s) is/are \( -1,6 \). (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The \( y \)-intercept is 36 . (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the \( x \)-axis at each \( x \)-intercept. The zero(s) of \( f \) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)

Graph the polynomial function \( f(x)=2 x^{4}+12 x^{3}-18 x^{2}-108 x \). Answer parts (a) through (e). (d) Determine the maximum number of turning points on the graph of the function. The graph of the function will have at most (e) Use the information in parts (a) through (d) to draw a complete graph of the function by hand. Choose the

91. \( f(\theta)=\frac{6\left(2-\theta^{3}\right)}{3-2 \theta} \)

Approximate the area under the graph of \( f(x) \) and above the \( x \)-axis using \( n \) rectangles. \( f(x)=x^{2}+2 \); interval \( [0,5] ; n=5 \); use left endpoints A. 40 B. 32 C. 65 D. 66

Find the integral. \( \int\left(x^{4}-2 x^{3}\right)^{4}\left(4 x^{3}-6 x^{2}\right) d x \)