When is substituted in

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

When u=2x+π3u=2x+\dfrac{\pi}{3} is substituted in ∫0π ⁣cos⁡(2x+π3) dx\displaystyle \int_{0}^{\pi}\!\cos(2x+\tfrac{\pi}{3})\,dx, which of the following gives the correct new limits of integration (ulower,uupper)(u_\text{lower},u_\text{upper})? (a) (π3, 5π3)\bigl(\dfrac{\pi}{3},\,\dfrac{5\pi}{3}\bigr) (b) (0,2π)(0,2\pi) (c) (π3, 7π3)\bigl(\dfrac{\pi}{3},\,\dfrac{7\pi}{3}\bigr) (d) (π3, 4π3)\bigl(\dfrac{\pi}{3},\,\dfrac{4\pi}{3}\bigr)

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