Theorem of Definite Integrals and its Properties
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Integral Calculus

86481 \(\int_{0}^{a} \sqrt{\frac{x}{a-x}} d x=\)

1 \(\left(\frac{\pi}{4}\right) \mathrm{a}\)
2 \(2 \pi \mathrm{a}\)
3 \(\left(\frac{\pi}{2}\right) \mathrm{a}\)
4 \(\pi \mathrm{a}\)
MHT CET-2020
Integral Calculus

86482 \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)

1 \(\left(\frac{1}{3}\right) \log \left(\frac{8}{3}\right)\)
2 \(\left(\frac{-1}{3}\right) \log \left(\frac{8}{3}\right)\)
3 \(\left(\frac{1}{2}\right) \log \left(\frac{8}{3}\right)\)
4 \(\left(\frac{-1}{2}\right) \log \left(\frac{8}{3}\right)\)
MHT CET-2020
Integral Calculus

86483 \(\int_{0}^{\frac{\pi}{2}}\left(e^{\sin x}-e^{\cos x}\right) d x=\)

1 1
2 0
3 \(\frac{1}{2}\)
4 \(\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86484 \(\int_{0}^{1} \frac{x^{2}}{1+x^{2}} d x=\)

1 \(1-\frac{\pi}{2}\)
2 \(1+\frac{\pi}{4}\)
3 \(1+\frac{\pi}{2}\)
4 \(1-\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86486 \(\int_{0}^{1} \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right) d x=\)

1 \(\frac{\pi}{2}+\log 2\)
2 \(\pi-\log 2\)
3 \(\frac{\pi}{2}-\log 2\)
4 \(\pi+\log 2\)
[МHT CET-2020]
NEET DIGITAL LIBRARY
Integral Calculus

86481 \(\int_{0}^{a} \sqrt{\frac{x}{a-x}} d x=\)

1 \(\left(\frac{\pi}{4}\right) \mathrm{a}\)
2 \(2 \pi \mathrm{a}\)
3 \(\left(\frac{\pi}{2}\right) \mathrm{a}\)
4 \(\pi \mathrm{a}\)
MHT CET-2020
Integral Calculus

86482 \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)

1 \(\left(\frac{1}{3}\right) \log \left(\frac{8}{3}\right)\)
2 \(\left(\frac{-1}{3}\right) \log \left(\frac{8}{3}\right)\)
3 \(\left(\frac{1}{2}\right) \log \left(\frac{8}{3}\right)\)
4 \(\left(\frac{-1}{2}\right) \log \left(\frac{8}{3}\right)\)
MHT CET-2020
Integral Calculus

86483 \(\int_{0}^{\frac{\pi}{2}}\left(e^{\sin x}-e^{\cos x}\right) d x=\)

1 1
2 0
3 \(\frac{1}{2}\)
4 \(\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86484 \(\int_{0}^{1} \frac{x^{2}}{1+x^{2}} d x=\)

1 \(1-\frac{\pi}{2}\)
2 \(1+\frac{\pi}{4}\)
3 \(1+\frac{\pi}{2}\)
4 \(1-\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86486 \(\int_{0}^{1} \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right) d x=\)

1 \(\frac{\pi}{2}+\log 2\)
2 \(\pi-\log 2\)
3 \(\frac{\pi}{2}-\log 2\)
4 \(\pi+\log 2\)
[МHT CET-2020]
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Integral Calculus

86481 \(\int_{0}^{a} \sqrt{\frac{x}{a-x}} d x=\)

1 \(\left(\frac{\pi}{4}\right) \mathrm{a}\)
2 \(2 \pi \mathrm{a}\)
3 \(\left(\frac{\pi}{2}\right) \mathrm{a}\)
4 \(\pi \mathrm{a}\)
MHT CET-2020
Integral Calculus

86482 \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)

1 \(\left(\frac{1}{3}\right) \log \left(\frac{8}{3}\right)\)
2 \(\left(\frac{-1}{3}\right) \log \left(\frac{8}{3}\right)\)
3 \(\left(\frac{1}{2}\right) \log \left(\frac{8}{3}\right)\)
4 \(\left(\frac{-1}{2}\right) \log \left(\frac{8}{3}\right)\)
MHT CET-2020
Integral Calculus

86483 \(\int_{0}^{\frac{\pi}{2}}\left(e^{\sin x}-e^{\cos x}\right) d x=\)

1 1
2 0
3 \(\frac{1}{2}\)
4 \(\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86484 \(\int_{0}^{1} \frac{x^{2}}{1+x^{2}} d x=\)

1 \(1-\frac{\pi}{2}\)
2 \(1+\frac{\pi}{4}\)
3 \(1+\frac{\pi}{2}\)
4 \(1-\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86486 \(\int_{0}^{1} \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right) d x=\)

1 \(\frac{\pi}{2}+\log 2\)
2 \(\pi-\log 2\)
3 \(\frac{\pi}{2}-\log 2\)
4 \(\pi+\log 2\)
[МHT CET-2020]
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Integral Calculus

86481 \(\int_{0}^{a} \sqrt{\frac{x}{a-x}} d x=\)

1 \(\left(\frac{\pi}{4}\right) \mathrm{a}\)
2 \(2 \pi \mathrm{a}\)
3 \(\left(\frac{\pi}{2}\right) \mathrm{a}\)
4 \(\pi \mathrm{a}\)
MHT CET-2020
Integral Calculus

86482 \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)

1 \(\left(\frac{1}{3}\right) \log \left(\frac{8}{3}\right)\)
2 \(\left(\frac{-1}{3}\right) \log \left(\frac{8}{3}\right)\)
3 \(\left(\frac{1}{2}\right) \log \left(\frac{8}{3}\right)\)
4 \(\left(\frac{-1}{2}\right) \log \left(\frac{8}{3}\right)\)
MHT CET-2020
Integral Calculus

86483 \(\int_{0}^{\frac{\pi}{2}}\left(e^{\sin x}-e^{\cos x}\right) d x=\)

1 1
2 0
3 \(\frac{1}{2}\)
4 \(\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86484 \(\int_{0}^{1} \frac{x^{2}}{1+x^{2}} d x=\)

1 \(1-\frac{\pi}{2}\)
2 \(1+\frac{\pi}{4}\)
3 \(1+\frac{\pi}{2}\)
4 \(1-\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86486 \(\int_{0}^{1} \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right) d x=\)

1 \(\frac{\pi}{2}+\log 2\)
2 \(\pi-\log 2\)
3 \(\frac{\pi}{2}-\log 2\)
4 \(\pi+\log 2\)
[МHT CET-2020]
NEET DIGITAL LIBRARY
Integral Calculus

86481 \(\int_{0}^{a} \sqrt{\frac{x}{a-x}} d x=\)

1 \(\left(\frac{\pi}{4}\right) \mathrm{a}\)
2 \(2 \pi \mathrm{a}\)
3 \(\left(\frac{\pi}{2}\right) \mathrm{a}\)
4 \(\pi \mathrm{a}\)
MHT CET-2020
Integral Calculus

86482 \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)

1 \(\left(\frac{1}{3}\right) \log \left(\frac{8}{3}\right)\)
2 \(\left(\frac{-1}{3}\right) \log \left(\frac{8}{3}\right)\)
3 \(\left(\frac{1}{2}\right) \log \left(\frac{8}{3}\right)\)
4 \(\left(\frac{-1}{2}\right) \log \left(\frac{8}{3}\right)\)
MHT CET-2020
Integral Calculus

86483 \(\int_{0}^{\frac{\pi}{2}}\left(e^{\sin x}-e^{\cos x}\right) d x=\)

1 1
2 0
3 \(\frac{1}{2}\)
4 \(\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86484 \(\int_{0}^{1} \frac{x^{2}}{1+x^{2}} d x=\)

1 \(1-\frac{\pi}{2}\)
2 \(1+\frac{\pi}{4}\)
3 \(1+\frac{\pi}{2}\)
4 \(1-\frac{\pi}{4}\)
MHT CET-2020
Integral Calculus

86486 \(\int_{0}^{1} \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right) d x=\)

1 \(\frac{\pi}{2}+\log 2\)
2 \(\pi-\log 2\)
3 \(\frac{\pi}{2}-\log 2\)
4 \(\pi+\log 2\)
[МHT CET-2020]