Question Detail
Question
Evaluate ∫0π/4 sec²(x) e4tan(x) dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
Let u = 4tan(x).Then, du/dx = 4sec²(x), which means du = 4sec²(x) dx, or sec²(x) dx = du/4.Now, change the limits of integration for u:When x = 0, u = 4tan(0) = 0.When x = π/4, u = 4tan(π/4) = 4(1) = 4.Substitute these into the integral:∫04 eu (du/4) = (1/4) ∫04 eu du= (1/4) [eu]04= (1/4) (e⁴ - e⁰)= (1/4) (e⁴ - 1).
Hint
Use u-substitution with u as the exponent of e. Remember to change the limits of integration.