Definite Integral as Limit of a Sum
Integral Calculus

86432 If \(\int_{\sqrt{2}}^{k} \frac{1}{x \sqrt{x^{2}-1}} d x=\frac{\pi}{12}\), then what is the value of \(k\) ?

1 0
2 1
3 -2
4 2
Integral Calculus

86433 \(\int_{0}^{\pi / 2} \frac{(\sin x)^{2006}}{(\sin x)^{2006}+(\cos x)^{2006}} d x=\) ?

1 \(\frac{\pi}{2}\)
2 None of these
3 2006. \((\sin \mathrm{x})^{2007}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86434 \(\int_{0}^{1} \frac{1}{x+\sqrt{x}} d x=\)

1 \(\log 1\)
2 \(\log 2\)
3 \(\log 3\)
4 \(\log 4\)
Integral Calculus

86435 \(\int_{2}^{k}(2 x+1) d x=6\), then \(k=\)

1 -2
2 3
3 4
4 -3
Integral Calculus

86432 If \(\int_{\sqrt{2}}^{k} \frac{1}{x \sqrt{x^{2}-1}} d x=\frac{\pi}{12}\), then what is the value of \(k\) ?

1 0
2 1
3 -2
4 2
Integral Calculus

86433 \(\int_{0}^{\pi / 2} \frac{(\sin x)^{2006}}{(\sin x)^{2006}+(\cos x)^{2006}} d x=\) ?

1 \(\frac{\pi}{2}\)
2 None of these
3 2006. \((\sin \mathrm{x})^{2007}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86434 \(\int_{0}^{1} \frac{1}{x+\sqrt{x}} d x=\)

1 \(\log 1\)
2 \(\log 2\)
3 \(\log 3\)
4 \(\log 4\)
Integral Calculus

86435 \(\int_{2}^{k}(2 x+1) d x=6\), then \(k=\)

1 -2
2 3
3 4
4 -3
Integral Calculus

86432 If \(\int_{\sqrt{2}}^{k} \frac{1}{x \sqrt{x^{2}-1}} d x=\frac{\pi}{12}\), then what is the value of \(k\) ?

1 0
2 1
3 -2
4 2
Integral Calculus

86433 \(\int_{0}^{\pi / 2} \frac{(\sin x)^{2006}}{(\sin x)^{2006}+(\cos x)^{2006}} d x=\) ?

1 \(\frac{\pi}{2}\)
2 None of these
3 2006. \((\sin \mathrm{x})^{2007}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86434 \(\int_{0}^{1} \frac{1}{x+\sqrt{x}} d x=\)

1 \(\log 1\)
2 \(\log 2\)
3 \(\log 3\)
4 \(\log 4\)
Integral Calculus

86435 \(\int_{2}^{k}(2 x+1) d x=6\), then \(k=\)

1 -2
2 3
3 4
4 -3
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Integral Calculus

86432 If \(\int_{\sqrt{2}}^{k} \frac{1}{x \sqrt{x^{2}-1}} d x=\frac{\pi}{12}\), then what is the value of \(k\) ?

1 0
2 1
3 -2
4 2
Integral Calculus

86433 \(\int_{0}^{\pi / 2} \frac{(\sin x)^{2006}}{(\sin x)^{2006}+(\cos x)^{2006}} d x=\) ?

1 \(\frac{\pi}{2}\)
2 None of these
3 2006. \((\sin \mathrm{x})^{2007}\)
4 \(\frac{\pi}{4}\)
Integral Calculus

86434 \(\int_{0}^{1} \frac{1}{x+\sqrt{x}} d x=\)

1 \(\log 1\)
2 \(\log 2\)
3 \(\log 3\)
4 \(\log 4\)
Integral Calculus

86435 \(\int_{2}^{k}(2 x+1) d x=6\), then \(k=\)

1 -2
2 3
3 4
4 -3