Definite Integral as Limit of a Sum
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Integral Calculus

86450 \(\int_{2016}^{2017} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4033-x}} d x\) is equal to

1 \(1 / 4\)
2 \(3 / 2\)
3 \(2017 / 2\)
4 \(1 / 2\)
5 508
Kerala CEE-2017
Integral Calculus

86451 \(\int_{0}^{\pi / 2} \log \left(\frac{\cos x}{\sin x}\right) d x\) is equal to

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(2 \pi\)
5 0
Kerala CEE-2016
Integral Calculus

86452 \(\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} d x\) is equal to

1 \(\frac{1}{5}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
2 \(\frac{1}{9}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
3 \(\frac{1}{4}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
4 \(\frac{1}{9}\left[\frac{1}{5} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
5 \(\frac{1}{9}\left[\frac{3}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{4}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
Kerala CEE-2015
Integral Calculus

86453 The value of \(\int_{0}^{1} \sqrt{x} e^{\sqrt{x}} d x\) is equal to

1 \(\frac{(\mathrm{e}-2)}{2}\)
2 \(2(\mathrm{e}-2)\)
3 \(2 \mathrm{e}-1\)
4 \(2(\mathrm{e}-1)\)
5 \(\frac{\mathrm{e}-1}{2}\)
Kerala CEE-2012
NEET DIGITAL LIBRARY
Integral Calculus

86450 \(\int_{2016}^{2017} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4033-x}} d x\) is equal to

1 \(1 / 4\)
2 \(3 / 2\)
3 \(2017 / 2\)
4 \(1 / 2\)
5 508
Kerala CEE-2017
Integral Calculus

86451 \(\int_{0}^{\pi / 2} \log \left(\frac{\cos x}{\sin x}\right) d x\) is equal to

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(2 \pi\)
5 0
Kerala CEE-2016
Integral Calculus

86452 \(\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} d x\) is equal to

1 \(\frac{1}{5}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
2 \(\frac{1}{9}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
3 \(\frac{1}{4}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
4 \(\frac{1}{9}\left[\frac{1}{5} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
5 \(\frac{1}{9}\left[\frac{3}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{4}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
Kerala CEE-2015
Integral Calculus

86453 The value of \(\int_{0}^{1} \sqrt{x} e^{\sqrt{x}} d x\) is equal to

1 \(\frac{(\mathrm{e}-2)}{2}\)
2 \(2(\mathrm{e}-2)\)
3 \(2 \mathrm{e}-1\)
4 \(2(\mathrm{e}-1)\)
5 \(\frac{\mathrm{e}-1}{2}\)
Kerala CEE-2012
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Integral Calculus

86450 \(\int_{2016}^{2017} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4033-x}} d x\) is equal to

1 \(1 / 4\)
2 \(3 / 2\)
3 \(2017 / 2\)
4 \(1 / 2\)
5 508
Kerala CEE-2017
Integral Calculus

86451 \(\int_{0}^{\pi / 2} \log \left(\frac{\cos x}{\sin x}\right) d x\) is equal to

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(2 \pi\)
5 0
Kerala CEE-2016
Integral Calculus

86452 \(\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} d x\) is equal to

1 \(\frac{1}{5}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
2 \(\frac{1}{9}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
3 \(\frac{1}{4}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
4 \(\frac{1}{9}\left[\frac{1}{5} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
5 \(\frac{1}{9}\left[\frac{3}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{4}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
Kerala CEE-2015
Integral Calculus

86453 The value of \(\int_{0}^{1} \sqrt{x} e^{\sqrt{x}} d x\) is equal to

1 \(\frac{(\mathrm{e}-2)}{2}\)
2 \(2(\mathrm{e}-2)\)
3 \(2 \mathrm{e}-1\)
4 \(2(\mathrm{e}-1)\)
5 \(\frac{\mathrm{e}-1}{2}\)
Kerala CEE-2012
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Integral Calculus

86450 \(\int_{2016}^{2017} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4033-x}} d x\) is equal to

1 \(1 / 4\)
2 \(3 / 2\)
3 \(2017 / 2\)
4 \(1 / 2\)
5 508
Kerala CEE-2017
Integral Calculus

86451 \(\int_{0}^{\pi / 2} \log \left(\frac{\cos x}{\sin x}\right) d x\) is equal to

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\pi\)
4 \(2 \pi\)
5 0
Kerala CEE-2016
Integral Calculus

86452 \(\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} d x\) is equal to

1 \(\frac{1}{5}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
2 \(\frac{1}{9}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
3 \(\frac{1}{4}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
4 \(\frac{1}{9}\left[\frac{1}{5} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
5 \(\frac{1}{9}\left[\frac{3}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{4}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
Kerala CEE-2015
Integral Calculus

86453 The value of \(\int_{0}^{1} \sqrt{x} e^{\sqrt{x}} d x\) is equal to

1 \(\frac{(\mathrm{e}-2)}{2}\)
2 \(2(\mathrm{e}-2)\)
3 \(2 \mathrm{e}-1\)
4 \(2(\mathrm{e}-1)\)
5 \(\frac{\mathrm{e}-1}{2}\)
Kerala CEE-2012