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`
Advertisements
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
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that \[\int_a^b xf\left( x \right)dx = \frac{a + b}{2} \int_a^b f\left( x \right)dx\]
If f (x) is a continuous function defined on [0, 2a]. Then, prove that
If \[\int\limits_0^1 \left( 3 x^2 + 2x + k \right) dx = 0,\] find the value of k.
Given that \[\int\limits_0^\infty \frac{x^2}{\left( x^2 + a^2 \right)\left( x^2 + b^2 \right)\left( x^2 + c^2 \right)} dx = \frac{\pi}{2\left( a + b \right)\left( b + c \right)\left( c + a \right)},\] the value of \[\int\limits_0^\infty \frac{dx}{\left( x^2 + 4 \right)\left( x^2 + 9 \right)},\]
\[\int\limits_0^{\pi/2} \frac{\cos x}{1 + \sin^2 x} dx\]
Evaluate the following integrals :-
\[\int_2^4 \frac{x^2 + x}{\sqrt{2x + 1}}dx\]
\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
\[\int\limits_{- 1}^1 e^{2x} dx\]
\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]
Evaluate the following using properties of definite integral:
`int_(- pi/4)^(pi/4) x^3 cos^3 x "d"x`
Evaluate the following using properties of definite integral:
`int_0^1 log (1/x - 1) "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 x^2 "d"x`
Find `int sqrt(10 - 4x + 4x^2) "d"x`
Find: `int logx/(1 + log x)^2 dx`
