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 ▸A block of temperature H=80ºC sits in a room of constant temperature T=20ºC at time t=0. At time t=12, the block has temperature H=50ºC. The rate of change of temperature of the block (dH/dt) is proportional to the temperature difference of the block ...
Find the roots of this equation: y=(8-x)lnx
Why does the second derivative tell us something about a function?
Integral of a compound equation (or otherwise finding the area under a graph): f(x) = 10x*(x^(0.5) - 2)