Integrals of powers of sine and cosine practice problems
∫ sinᵐx cosⁿx dx: save one factor when a power is odd, use half-angle identities when both are even. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Evaluate \( \displaystyle \int_0^{\pi} \cos^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int \sin{\left(x \right)} \cos^{4}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int \cos^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int \sin^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int_0^{\pi} \sin^{5}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int_0^{\pi} \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx \).
Evaluate \( \displaystyle \int_0^{\frac{\pi}{2}} \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx \).