Integrate x^2sin(x) between -pi and pi
It is possible to solve this question using integration by parts. However, we note that sin(x) is an odd function, meaning that sin(-x) = -sin(x). Thus x2sin(x) is also an odd function. This means that the area under x2sin(x) from 0 to pi is equal to the area under x2sin(x) from -pi to 0. Hence the integral of x2sin(x) between -pi and pi is 0.
HL
Answered by Harry L. • Further Mathematics tutor
7900 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.
Prove by induction that, for all integers n >=1 , ∑(from r=1 to n) r(2r−1)(3r−1)=(n/6)(n+1)(9n^2 -n−2). Assume that 9(k+1)^2 -(k+1)-2=9k^2 +17k+6
For what values of x is Cosh^2(x) - Sinh(x) = 5 Give your answer in the form of a logarithm
Prove by induction that 2^(6n)+3^(2n-2) is divsible by 5. (AS Further pure)