MCQs of Integrals

Showing 241 to 250 out of 421 Questions

241.

I_{n} = \int_{0}^{\frac{π}{4}} \tan^{n} x d x

then

\underset{n \to \infty}{l i m} n [I_{n} + I_{n - 2}]

equals

242.

\int_{0}^{2} [x^{2}] d x

= _____

243.

\int_{- π}^{π} \frac{2 x (1 + \sin x)}{1 + \cos^{2} x} d x

244.

If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then

\int_{0}^{2} x f^{'} (x) d x

= _____

245.

If f(a + b - x) = f(x) then

\int_{a}^{b} x f (x) d x

is equal to

246.

\underset{n \to \infty}{l i m} \frac{1 + 2^{4} + 3^{4} + . . . + n^{4}}{n^{5}} - \underset{n \to \infty}{l i m} \frac{1 + 2^{3} + 3^{3} + . . . + n^{3}}{n^{5}}

= _____

247.

\underset{x \to 0}{l i m} \frac{\int_{0}^{x^{2}} s e c^{2} t d t}{x \sin x}

= _____

248.

\lim_{n \to \infty} \sum_{r = 1}^{n} \frac{1}{n} e^{\frac{r}{n}}

= _____

249.

The value of

\int_{- 2}^{3} |1 - x^{2}| d x

250.

The value of

I = \int_{0}^{\frac{π}{2}} \frac{(\sin x + \cos x)^{2}}{\sqrt{1 + \sin 2 x}} d x

Showing 241 to 250 out of 421 Questions