Integrate sin(x)cos(x)^2 from 0 to π/2
Use substitution u=cos(x) resulting in du=-sin(x)dx: ∫0π/2sin(x)cos(x)^2dx = ∫0π/2-u^2du = [-1/3 u^3]x=0x=π/2 = [-1/3 cos(x)^3]0π/2 = (-1/3 cos(π/2)^3) - (-1/3 cos(0)^3) = (-1/3 0^3 ) - (-1/3 1^3) = 0 + 1/3 = 1/3
BS
Related Maths A Level answers
All answers ▸Find the solution of the differential equation: dy/dx = (xy^2 + x)/y. There is no need to rearrange the solution to be in terms of y.
An open-topped fish tank is to be made for an aquarium. It will have a square base, rectangular sides, and a volume of 60 m3. The base materials cost £15 per m2 and the sides £8 per m2. What should the height be to minimise costs?
What are radians, why can't we just use degrees?
How can you integrate ln(x) with respect to x?