NDA MATHEMATICS QUIZ - 26

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Question 1:

Value of $\int_{0}^{\frac{\pi}{2}} \cos x \cdot e^{\sin x} \cdot d x$ is

Question 2:

If $I_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x$ then for any positive integer $\mathrm{n}$, The value of $L_{n \rightarrow \infty} n\left(\mathrm{I}_{n}+\mathrm{I}_{n}-2\right)$ is equal to

Question 3:

$\int_{-2}^{2}|x| d x=$ . . . . . . . .

Question 4:

$\int_{0}^{\pi}|\cos \theta-\sin \theta| d \theta$ equals

Question 5:

If $\int_{0}^{\pi} x f(\sin x) d x=k \int_{0}^{\frac{\pi}{2}} f(\sin x) d x$ then $\mathrm{k}$ equals

Question 6:

$\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x \cdot d x}{\cos ^{\frac{3}{2}} x+\sin ^{\frac{3}{2}} x}=\ldots \ldots$

Question 7:

$\int_{0}^{1-5}\left[x^{2}\right] d x=\ldots$

Question 8:

Value of the integral $\int_{1}^{\sqrt{e}} t \log d t$ is

Question 9:

$\int_{0}^{\pi} \frac{x d x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x}=\ldots \ldots \ldots ?$

Question 10:

If $\int_{0}^{\infty} \frac{\log \left(1+x^{2}\right) d x}{1+x^{2}}=\pi \log \mathrm{k}$ then $\mathrm{k}$ equals

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