Advertisements
Advertisements
Question
Using second fundamental theorem, evaluate the following:
`int_0^1 "e"^(2x) "d"x`
Sum
Solution
`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
Definite Integrals
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\limits_0^4 \frac{1}{\sqrt{4x - x^2}} dx\]
\[\int\limits_1^2 \frac{1}{x \left( 1 + \log x \right)^2} dx\]
\[\int\limits_0^{\pi/2} \cos^5 x\ dx\]
If `f` is an integrable function such that f(2a − x) = f(x), then prove that
\[\int\limits_0^{2a} f\left( x \right) dx = 2 \int\limits_0^a f\left( x \right) dx\]
\[\int\limits_1^3 \left( 2x + 3 \right) dx\]
\[\int\limits_0^5 \left( x + 1 \right) dx\]
\[\int\limits_0^{\pi/2} \left| \sin x - \cos x \right| dx\]
Integrate `((2"a")/sqrt(x) - "b"/x^2 + 3"c"root(3)(x^2))` w.r.t. x
Verify the following:
`int (2x + 3)/(x^2 + 3x) "d"x = log|x^2 + 3x| + "C"`
`int "e"^x ((1 - x)/(1 + x^2))^2 "d"x` is equal to ______.
