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Statement I: attains its maximum value at on
MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals
Problem Statement I: ϕ ( x ) = ∫ 0 x ( 3 sin t + 4 cos t ) d t \phi(x)=\int_0^x(3\sin t+4\cos t)\,dt ϕ ( x ) = ∫ 0 x ( 3 sin t + 4 cos t ) d t attains its maximum value at x = π 3 x=\frac{\pi}{3} x = 3 π on [ π 6 , π 3 ] \left[\frac{\pi}{6},\frac{\pi}{3}\right] [ 6 π , 3 π ] . Statement II: ϕ ( x ) = ∫ 0 x ( 3 sin t + 4 cos t ) d t \phi(x)=\int_0^x(3\sin t+4\cos t)\,dt ϕ ( x ) = ∫ 0 x ( 3 sin t + 4 cos t ) d t is an increasing function on [ π 6 , π 3 ] \left[\frac{\pi}{6},\frac{\pi}{3}\right] [ 6 π , 3 π ] .
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