Find the integral of (cosx)*(sinx)^2 with respect to x
This is a common example of an integral that is a product of two functions whose derivatives are related. As we know the derivative of sinx is cosx, we can use substitution to easily solve this - let our U= sinx, and dU/dx = cosx so dU = cosxdx. Input the substitution to give the integral of U2dU, which by the power rule is simply solved as U3/3, without forgetting the constant C. Substituting U we find that the final answer is (sin3x)/3 + C
HS
Related Maths A Level answers
All answers ▸How can I find the equation of a line l which passes through the points (5,7) and (3, -1)
What is a stationary point on a curve? How do I calculate the co-ordinates of a stationary point?
How do I find the stationary points on the curve y = f(x) = x^3+6x^2-36x?
Differentiate the function f(x) = x^2 * e^2x with respect to x