Theorem of Definite Integrals and its Properties
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Integral Calculus

86462 \(\int_{0}^{\pi / 2} \log (\tan x) d x\)

1 zero
2 2
3 \(\pi / 3\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86463 The value of \(\int_{-1}^{3}\left[\tan ^{-1}\left(\frac{x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right] d x\) is :

1 \(2 \pi\)
2 \(\pi\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86464 The value of \(\int_{0}^{\pi} \frac{d x}{5+3 \cos x}\) is :

1 \(\pi / 4\)
2 \(\pi / 8\)
3 \(\pi / 2\)
4 zero
Karnataka CET-2002
Integral Calculus

86466 If \(I_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x\), where \(n\) is positive integer, than \(I_{10}+I_{8}\) is equal to

1 9
2 \(\frac{1}{7}\)
3 \(\frac{1}{8}\)
4 \(\frac{1}{9}\)
Karnataka CET-2021
Integral Calculus

86467 \(\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x\) is equal to

1 \(2(\sin x+x \cos \theta)+C\)
2 \(2(\sin x-x \cos \theta)+C\)
3 \(2(\sin x+2 x \cos \theta)+C\)
4 \(2(\sin x-2 x \cos \theta)+C\)
Karnataka CET-2017
Join With Us for More Updates
Integral Calculus

86462 \(\int_{0}^{\pi / 2} \log (\tan x) d x\)

1 zero
2 2
3 \(\pi / 3\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86463 The value of \(\int_{-1}^{3}\left[\tan ^{-1}\left(\frac{x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right] d x\) is :

1 \(2 \pi\)
2 \(\pi\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86464 The value of \(\int_{0}^{\pi} \frac{d x}{5+3 \cos x}\) is :

1 \(\pi / 4\)
2 \(\pi / 8\)
3 \(\pi / 2\)
4 zero
Karnataka CET-2002
Integral Calculus

86466 If \(I_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x\), where \(n\) is positive integer, than \(I_{10}+I_{8}\) is equal to

1 9
2 \(\frac{1}{7}\)
3 \(\frac{1}{8}\)
4 \(\frac{1}{9}\)
Karnataka CET-2021
Integral Calculus

86467 \(\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x\) is equal to

1 \(2(\sin x+x \cos \theta)+C\)
2 \(2(\sin x-x \cos \theta)+C\)
3 \(2(\sin x+2 x \cos \theta)+C\)
4 \(2(\sin x-2 x \cos \theta)+C\)
Karnataka CET-2017
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Integral Calculus

86462 \(\int_{0}^{\pi / 2} \log (\tan x) d x\)

1 zero
2 2
3 \(\pi / 3\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86463 The value of \(\int_{-1}^{3}\left[\tan ^{-1}\left(\frac{x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right] d x\) is :

1 \(2 \pi\)
2 \(\pi\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86464 The value of \(\int_{0}^{\pi} \frac{d x}{5+3 \cos x}\) is :

1 \(\pi / 4\)
2 \(\pi / 8\)
3 \(\pi / 2\)
4 zero
Karnataka CET-2002
Integral Calculus

86466 If \(I_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x\), where \(n\) is positive integer, than \(I_{10}+I_{8}\) is equal to

1 9
2 \(\frac{1}{7}\)
3 \(\frac{1}{8}\)
4 \(\frac{1}{9}\)
Karnataka CET-2021
Integral Calculus

86467 \(\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x\) is equal to

1 \(2(\sin x+x \cos \theta)+C\)
2 \(2(\sin x-x \cos \theta)+C\)
3 \(2(\sin x+2 x \cos \theta)+C\)
4 \(2(\sin x-2 x \cos \theta)+C\)
Karnataka CET-2017
NEET DIGITAL LIBRARY
Integral Calculus

86462 \(\int_{0}^{\pi / 2} \log (\tan x) d x\)

1 zero
2 2
3 \(\pi / 3\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86463 The value of \(\int_{-1}^{3}\left[\tan ^{-1}\left(\frac{x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right] d x\) is :

1 \(2 \pi\)
2 \(\pi\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86464 The value of \(\int_{0}^{\pi} \frac{d x}{5+3 \cos x}\) is :

1 \(\pi / 4\)
2 \(\pi / 8\)
3 \(\pi / 2\)
4 zero
Karnataka CET-2002
Integral Calculus

86466 If \(I_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x\), where \(n\) is positive integer, than \(I_{10}+I_{8}\) is equal to

1 9
2 \(\frac{1}{7}\)
3 \(\frac{1}{8}\)
4 \(\frac{1}{9}\)
Karnataka CET-2021
Integral Calculus

86467 \(\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x\) is equal to

1 \(2(\sin x+x \cos \theta)+C\)
2 \(2(\sin x-x \cos \theta)+C\)
3 \(2(\sin x+2 x \cos \theta)+C\)
4 \(2(\sin x-2 x \cos \theta)+C\)
Karnataka CET-2017
Join With Us for More Updates
Integral Calculus

86462 \(\int_{0}^{\pi / 2} \log (\tan x) d x\)

1 zero
2 2
3 \(\pi / 3\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86463 The value of \(\int_{-1}^{3}\left[\tan ^{-1}\left(\frac{x}{x^{2}+1}\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right] d x\) is :

1 \(2 \pi\)
2 \(\pi\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Karnataka CET-2000
Integral Calculus

86464 The value of \(\int_{0}^{\pi} \frac{d x}{5+3 \cos x}\) is :

1 \(\pi / 4\)
2 \(\pi / 8\)
3 \(\pi / 2\)
4 zero
Karnataka CET-2002
Integral Calculus

86466 If \(I_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x\), where \(n\) is positive integer, than \(I_{10}+I_{8}\) is equal to

1 9
2 \(\frac{1}{7}\)
3 \(\frac{1}{8}\)
4 \(\frac{1}{9}\)
Karnataka CET-2021
Integral Calculus

86467 \(\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x\) is equal to

1 \(2(\sin x+x \cos \theta)+C\)
2 \(2(\sin x-x \cos \theta)+C\)
3 \(2(\sin x+2 x \cos \theta)+C\)
4 \(2(\sin x-2 x \cos \theta)+C\)
Karnataka CET-2017