Advertisements
Advertisements
प्रश्न
Using second fundamental theorem, evaluate the following:
`int_0^1 "e"^(2x) "d"x`
योग
Advertisements
उत्तर
`int_0^1 "e"^(2x) "d"x = ["e"^(2x)/2]_0^1`
= `1/2 ["e"^(2x)]_0^1`
= `1/2["e"^(2(1)) - "e"^(2(0))]`
= `1/2 ["e"^2 - "e"^0]`
= `1/2 ["e"^2 - 1]`
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\limits_{- 1}^1 5 x^4 \sqrt{x^5 + 1} dx\]
\[\int\limits_{\pi/3}^{\pi/2} \frac{\sqrt{1 + \cos x}}{\left( 1 - \cos x \right)^{3/2}} dx\]
\[\int\limits_0^a x \sqrt{\frac{a^2 - x^2}{a^2 + x^2}} dx\]
If f(2a − x) = −f(x), prove that
\[\int\limits_0^{2a} f\left( x \right) dx = 0 .\]
\[\int\limits_{- 1}^1 \left( x + 3 \right) dx\]
\[\int\limits_0^{15} \left[ x \right] dx .\]
\[\int\limits_0^{\pi/2} \frac{1}{2 + \cos x} dx\] equals
\[\int\limits_0^{\pi/2} \frac{1}{1 + \tan x} dx\] is equal to
\[\int\limits_0^4 x dx\]
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
