Find the indefinite integral of sin(2x)(cos^2(x)) with respect to x.
We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)).
Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x).
We can now split the integral into the sum of two simpler ones with integrands 0.5sin(2x) and 0.5sin(2x)cos(2x), the latter of which is equal to 0.25sin(4x).
These integrate nicely to -0.25cos(2x)-(1/16)cos(4x) + c where c is the constant of integration.
PP
Related Maths A Level answers
All answers ▸Solve integral [3x^2 (x^3 + 1)^6] dx
I am struggling understanding how to differentiate negative indices. I get confused with the power increasing or decreasing.
How do I solve equations with modulus functions on both sides?
Find the first 3 terms and the sum to infinity of a geometric series with first term, 10 and common ratio 0.2