Advertisements
Advertisements
प्रश्न
Evaluate :
Advertisements
उत्तर
\[ = \left.\frac{3^x}{\log3}\right|_2^3 + C .............\left(Use: \int a^x = \frac{a^x}{\log a} + C\right)\]
\[ = \frac{3^3}{\log3} - \frac{3^2}{\log3} + C\]
\[= \frac{1}{\log3}( 3^3 - 3^2 ) + C\]
\[ = \frac{1}{\log3}(27 - 9) + C\]
\[ = \frac{1}{\log3}(18) + C\]
APPEARS IN
संबंधित प्रश्न
If f (x) is a continuous function defined on [0, 2a]. Then, prove that
The value of \[\int\limits_0^\pi \frac{x \tan x}{\sec x + \cos x} dx\] is __________ .
\[\int\limits_0^4 x\sqrt{4 - x} dx\]
\[\int\limits_1^5 \frac{x}{\sqrt{2x - 1}} dx\]
\[\int\limits_0^{\pi/2} x^2 \cos 2x dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]
\[\int\limits_{\pi/6}^{\pi/2} \frac{\ cosec x \cot x}{1 + {cosec}^2 x} dx\]
\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]
Using second fundamental theorem, evaluate the following:
`int_0^1 x"e"^(x^2) "d"x`
Using second fundamental theorem, evaluate the following:
`int_0^(pi/2) sqrt(1 + cos x) "d"x`
Using second fundamental theorem, evaluate the following:
`int_1^2 (x - 1)/x^2 "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 x^2 "d"x`
Choose the correct alternative:
`int_0^1 (2x + 1) "d"x` is
Evaluate `int "dx"/sqrt((x - alpha)(beta - x)), beta > alpha`
If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then ______.
Find: `int logx/(1 + log x)^2 dx`
If velocity changes with time, what does a definite integral give over a time interval?
