Advertisements
Advertisements
Question
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
Advertisements
Solution
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to e – 1.
Explanation:
Let I = `int_0^(pi/2) cos x "e"^(sinx) "d"x`
Put sin x = t
⇒ cos x "d"x` = dt
∴ I = `int_0^1 "e"^"t" "dt"`
= `["e"^"t"]_0^1`
= `"e"^1 - "e"^0`
= e – 1
APPEARS IN
RELATED QUESTIONS
Evaluate: `int_(-a)^asqrt((a-x)/(a+x)) dx`
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/4) log (1+ tan x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_((-pi)/2)^(pi/2) sin^2 x dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
Evaluate : `int "e"^(3"x")/("e"^(3"x") + 1)` dx
Prove that `int_0^"a" "f" ("x") "dx" = int_0^"a" "f" ("a" - "x") "d x",` hence evaluate `int_0^pi ("x" sin "x")/(1 + cos^2 "x") "dx"`
`int_"a"^"b" "f"(x) "d"x` = ______
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
Evaluate `int_1^3 x^2*log x "d"x`
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______
`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?
`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.
If `int_(-a)^a(|x| + |x - 2|)dx` = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then `int_a^(-a)(x + [x])dx` is equal to ______.
The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.
If f(x) = `{{:(x^2",", "where" 0 ≤ x < 1),(sqrt(x)",", "when" 1 ≤ x < 2):}`, then `int_0^2f(x)dx` equals ______.
Evaluate: `int_0^π 1/(5 + 4 cos x)dx`
`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
If `int_0^(π/2) log cos x dx = π/2 log(1/2)`, then `int_0^(π/2) log sec dx` = ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
Evaluate `int_0^(π//4) log (1 + tanx)dx`.
Evaluate: `int_0^π x/(1 + sinx)dx`.
Solve the following.
`int_0^1e^(x^2)x^3 dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 dx`
Solve.
`int_0^1e^(x^2)x^3dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
