Question

How do you do this on the calculator?

Answer 1

B) -3.464

Explanation:

∫₀³ g'(x) cos²(2g(x) + 1) dx

Using u substitution:

u = 2g(x) + 1

du = 2g'(x) dx

½ du = g'(x) dx

When x = 0, u = 11.

When x = 3, u = -3.

½ ∫₁₁⁻³ cos²(u) du

You can use a calculator to solve this, or you can evaluate algebraically.

Use power reduction formula:

½ ∫ (½ + ½ cos(2u)) du

¼ ∫ du + ¼ ∫ cos(2u) du

¼ ∫ du + ⅛ ∫ 2 cos(2u) du

¼ u + ⅛ sin(2u) + C

Evaluating from u = 11 to u = -3:

[¼ (-3) + ⅛ sin(-6) + C] − [¼ (11) + ⅛ sin(22) + C]

-⁷/₂ + ⅛ sin(-6) − ⅛ sin(22)

−3.464