Standard +0.3 This is a straightforward double integration by parts problem with clear structure: integrate x² sin x from 0 to π. While it requires two applications of integration by parts and careful handling of boundary terms, it follows a standard algorithmic approach with no conceptual surprises. The definite integral evaluation is routine, making this slightly easier than average.
Integrate by parts and reach \(\pm x^2 \cos x \pm \int 2x \cos x \, dx\)
M1
Obtain \(-x^2 \cos x + \int 2x \cos x \, dx\), or equivalent
A1
Complete the integration, obtaining \(-x^2 \cos x + 2x \sin x + 2 \cos x\), or equivalent
A1
Substitute limits correctly, having integrated twice
M1
Obtain the given answer correctly
A1
[5]
Integrate by parts and reach $\pm x^2 \cos x \pm \int 2x \cos x \, dx$ | M1 |
Obtain $-x^2 \cos x + \int 2x \cos x \, dx$, or equivalent | A1 |
Complete the integration, obtaining $-x^2 \cos x + 2x \sin x + 2 \cos x$, or equivalent | A1 |
Substitute limits correctly, having integrated twice | M1 |
Obtain the given answer correctly | A1 | [5]