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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Match the following columns: Column-I Column-II (A) ∫_0^ π /2 (...

Match the following columns:
Column-IColumn-II
(A) \displaystyle \int_0^{\pi/2}\frac{\cos x}{(1 + \sin x)(2 + \sin x)}dx=</td><td>(P)dx =</td><td>(P) \displaystyle\frac{\pi}{6}</td></tr><tr><td>(B)∫041π/4∣cos⁡x∣dx=</td></tr><tr><td>(B) \displaystyle \int_0^{41\pi/4} |\cos x| dx =(Q) \displaystyle 20 + 12\frac{1}{\sqrt{2}}
(C) \displaystyle \int_{-1/2}^{1/2} \left[ [x] + \ln \left( \frac{1 + x}{1 - x} \right) \right]dx=(where[dx = (where \displaystyle [\cdot]represents greatest integer function)</td><td>(R) \displaystyle \ln 4 - \ln 3</td></tr><tr><td>(D) \displaystyle \int_0^{\pi/2} 2cos⁡θ3(sin⁡θ+cos⁡θ)\frac{2\sqrt{\cos \theta}}{3(\sqrt{\sin \theta} + \sqrt{\cos \theta})}dθ=\theta =(S) \displaystyle -12</td></tr></table>\frac{1}{2}</td></tr></table>

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