[ \int e^ax \cos(bx) , dx ]
Problem 3: Indefinite Integral using Trigonometric Substitution Evaluate the integral:
I=π4cap I equals the fraction with numerator pi and denominator 4 end-fraction ✅ Result The value of the integral is
First, rewrite the integrand: $$ \sin^4(x) \cos^2(x) = (\sin^2(x))^2 \cos^2(x) $$ $$ = \left( \frac1 - \cos(2x)2 \right)^2 \left( \frac1 + \cos(2x)2 \right) $$
cap I equals negative the fraction with numerator pi and denominator 2 end-fraction l n 2 The value of the integral is
To illustrate the level of difficulty, here are two sample problems and their solution outlines that you would find in a top-tier advanced calculus PDF.
