Advertisements
Advertisements
प्रश्न
The value of `int_2^3 x/(x^2 + 1)`dx is ______.
विकल्प
`log 4`
`log 3/2`
`1/2 log2`
`log 9/4`
उत्तर
The value of `int_2^3 x/(x^2 + 1)`dx is `underline(bb(1/2 log 2))`.
Explanation:
`int_2^3 x/(x^2 + 1) = 1/2 [log(x^2 + 1)]_2^3`
= `1/2 (log 10 - log 5)`
= `1/2 log (10/5)`
= `1/2 log 2`
APPEARS IN
संबंधित प्रश्न
\[\int\limits_0^{( \pi )^{2/3}} \sqrt{x} \cos^2 x^{3/2} dx\]
\[\int\limits_1^4 f\left( x \right) dx, where f\left( x \right) = \begin{cases}7x + 3 & , & \text{if }1 \leq x \leq 3 \\ 8x & , & \text{if }3 \leq x \leq 4\end{cases}\]
Evaluate the following integral:
Prove that:
Evaluate each of the following integral:
Evaluate: \[\int\limits_{- \pi/2}^{\pi/2} \frac{\cos x}{1 + e^x}dx\] .
\[\int\limits_0^1 \frac{1 - x}{1 + x} dx\]
\[\int\limits_0^{15} \left[ x^2 \right] dx\]
\[\int\limits_0^4 x dx\]
\[\int\limits_{- 1}^1 e^{2x} dx\]
Prove that `int_a^b ƒ ("x") d"x" = int_a^bƒ(a + b - "x") d"x" and "hence evaluate" int_(π/6)^(π/3) (d"x")/(1+sqrt(tan "x")`
Evaluate the following integrals as the limit of the sum:
`int_1^3 (2x + 3) "d"x`
Choose the correct alternative:
`int_0^oo "e"^(-2x) "d"x` is
Choose the correct alternative:
If f(x) is a continuous function and a < c < b, then `int_"a"^"c" f(x) "d"x + int_"c"^"b" f(x) "d"x` is
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
