Step 2: = 4 tan−1(x) = 4 tan−1(−1) = 4 − 4 = 2π.- A Use u-substitution. Here, u = x^3 − 6 and du = 4x^2 dx. Then,
(^) ∫ 4 x^2 dx = ∫ u^9 du = + C. Replace u for the final solution:
- A Use the Mean Value Theorem for Integrals, f(c) = f (x) dx. Thus, for this problem, f(c)
= = .
- D Use the Second Fundamental Theorem of Calculus: f(t) dt = f (x). Thus, for this
problem, t^2 + 4t dt = 6x((3x^2 )^2 + 4(3x^2 )) = 54x^5 + 72 x^3.17. A First, rewrite the integral: dx = dx = ∫tan x dx. You can either derive the
integral from using u-substitution, or you should have memorized that ∫ tan x dx = − ln |
cosx | + C.- A The average value of the function f (x) = (x − 1)^2 on the interval from x = 1 to x = 5 is
Step 1: If you want to find the average value of f (x) on an interval [a, b], you need to evaluatethe integral f(x) dx.So here we would evaluate the integral dx.