Definite Integral as Limit of a Sum
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Integral Calculus

86375 \(\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x\)

1 1
2 3
3 2
4 0
MHT CET-2016
Integral Calculus

86437 If \(\int^{b} x^{3} d x=0\) and if \(\int^{b} x^{2} d x=\frac{2}{3}\), then \(a\) and \(b\) are respectively

1 1,1
2 -1.1
3 \(1,-1\)
4 1
MHT CET-2022
Integral Calculus

86379 \(\quad \int_{0}^{\pi / 2} \sin 2 x \cdot \log \tan x d x\) is equal to

1 0
2 2
3 4
4 7
VITEEE-2015
Integral Calculus

86380 If \(y+\sqrt{1+y^{2}}=e^{x}\), then the value of \(y\) is

1 \(e^{\mathrm{x}}-\mathrm{e}^{-\mathrm{x}}\)
2 \(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}}{2}\)
4 None of these
UPSEE-2018
Integral Calculus

86381 If \(\int_{0}^{t^{2}} \mathrm{x} f(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{2}{5} \mathrm{t}^{5}, \mathrm{t}>0\), then \(f\left(\frac{4}{25}\right)\) is

1 \(\frac{2}{5}\)
2 \(\frac{5}{2}\)
3 \(-\frac{2}{5}\)
4 None of these
UPSEE-2012
NEET DIGITAL LIBRARY
Integral Calculus

86375 \(\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x\)

1 1
2 3
3 2
4 0
MHT CET-2016
Integral Calculus

86437 If \(\int^{b} x^{3} d x=0\) and if \(\int^{b} x^{2} d x=\frac{2}{3}\), then \(a\) and \(b\) are respectively

1 1,1
2 -1.1
3 \(1,-1\)
4 1
MHT CET-2022
Integral Calculus

86379 \(\quad \int_{0}^{\pi / 2} \sin 2 x \cdot \log \tan x d x\) is equal to

1 0
2 2
3 4
4 7
VITEEE-2015
Integral Calculus

86380 If \(y+\sqrt{1+y^{2}}=e^{x}\), then the value of \(y\) is

1 \(e^{\mathrm{x}}-\mathrm{e}^{-\mathrm{x}}\)
2 \(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}}{2}\)
4 None of these
UPSEE-2018
Integral Calculus

86381 If \(\int_{0}^{t^{2}} \mathrm{x} f(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{2}{5} \mathrm{t}^{5}, \mathrm{t}>0\), then \(f\left(\frac{4}{25}\right)\) is

1 \(\frac{2}{5}\)
2 \(\frac{5}{2}\)
3 \(-\frac{2}{5}\)
4 None of these
UPSEE-2012
Join With Us for More Updates
Integral Calculus

86375 \(\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x\)

1 1
2 3
3 2
4 0
MHT CET-2016
Integral Calculus

86437 If \(\int^{b} x^{3} d x=0\) and if \(\int^{b} x^{2} d x=\frac{2}{3}\), then \(a\) and \(b\) are respectively

1 1,1
2 -1.1
3 \(1,-1\)
4 1
MHT CET-2022
Integral Calculus

86379 \(\quad \int_{0}^{\pi / 2} \sin 2 x \cdot \log \tan x d x\) is equal to

1 0
2 2
3 4
4 7
VITEEE-2015
Integral Calculus

86380 If \(y+\sqrt{1+y^{2}}=e^{x}\), then the value of \(y\) is

1 \(e^{\mathrm{x}}-\mathrm{e}^{-\mathrm{x}}\)
2 \(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}}{2}\)
4 None of these
UPSEE-2018
Integral Calculus

86381 If \(\int_{0}^{t^{2}} \mathrm{x} f(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{2}{5} \mathrm{t}^{5}, \mathrm{t}>0\), then \(f\left(\frac{4}{25}\right)\) is

1 \(\frac{2}{5}\)
2 \(\frac{5}{2}\)
3 \(-\frac{2}{5}\)
4 None of these
UPSEE-2012
For More Updates join with Us
Integral Calculus

86375 \(\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x\)

1 1
2 3
3 2
4 0
MHT CET-2016
Integral Calculus

86437 If \(\int^{b} x^{3} d x=0\) and if \(\int^{b} x^{2} d x=\frac{2}{3}\), then \(a\) and \(b\) are respectively

1 1,1
2 -1.1
3 \(1,-1\)
4 1
MHT CET-2022
Integral Calculus

86379 \(\quad \int_{0}^{\pi / 2} \sin 2 x \cdot \log \tan x d x\) is equal to

1 0
2 2
3 4
4 7
VITEEE-2015
Integral Calculus

86380 If \(y+\sqrt{1+y^{2}}=e^{x}\), then the value of \(y\) is

1 \(e^{\mathrm{x}}-\mathrm{e}^{-\mathrm{x}}\)
2 \(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}}{2}\)
4 None of these
UPSEE-2018
Integral Calculus

86381 If \(\int_{0}^{t^{2}} \mathrm{x} f(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{2}{5} \mathrm{t}^{5}, \mathrm{t}>0\), then \(f\left(\frac{4}{25}\right)\) is

1 \(\frac{2}{5}\)
2 \(\frac{5}{2}\)
3 \(-\frac{2}{5}\)
4 None of these
UPSEE-2012
NEET DIGITAL LIBRARY
Integral Calculus

86375 \(\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin x}{2+\sin x}\right) d x\)

1 1
2 3
3 2
4 0
MHT CET-2016
Integral Calculus

86437 If \(\int^{b} x^{3} d x=0\) and if \(\int^{b} x^{2} d x=\frac{2}{3}\), then \(a\) and \(b\) are respectively

1 1,1
2 -1.1
3 \(1,-1\)
4 1
MHT CET-2022
Integral Calculus

86379 \(\quad \int_{0}^{\pi / 2} \sin 2 x \cdot \log \tan x d x\) is equal to

1 0
2 2
3 4
4 7
VITEEE-2015
Integral Calculus

86380 If \(y+\sqrt{1+y^{2}}=e^{x}\), then the value of \(y\) is

1 \(e^{\mathrm{x}}-\mathrm{e}^{-\mathrm{x}}\)
2 \(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{x}}}{2}\)
4 None of these
UPSEE-2018
Integral Calculus

86381 If \(\int_{0}^{t^{2}} \mathrm{x} f(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{2}{5} \mathrm{t}^{5}, \mathrm{t}>0\), then \(f\left(\frac{4}{25}\right)\) is

1 \(\frac{2}{5}\)
2 \(\frac{5}{2}\)
3 \(-\frac{2}{5}\)
4 None of these
UPSEE-2012