Statement I: attains its maximum value at on

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Statement I: ϕ(x)=∫0x(3sin⁡t+4cos⁡t) dt\phi(x)=\int_0^x(3\sin t+4\cos t)\,dt attains its maximum value at x=π3x=\frac{\pi}{3} on [π6,π3]\left[\frac{\pi}{6},\frac{\pi}{3}\right]. Statement II: ϕ(x)=∫0x(3sin⁡t+4cos⁡t) dt\phi(x)=\int_0^x(3\sin t+4\cos t)\,dt is an increasing function on [π6,π3]\left[\frac{\pi}{6},\frac{\pi}{3}\right].

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