Advertisements
Advertisements
प्रश्न
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
उत्तर
We have I = `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
= `int_0^(pi/4) sqrt((sinx + cosx)^2) "d"x`
= `int_0^(pi/4) (sinx + cosx) "d"x`
= `(-cosx + sinx)_0^(pi/4)`
I = 1.
APPEARS IN
संबंधित प्रश्न
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) cos^2 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 (x dx)/(1+ sin x)`
Evaluate`int (1)/(x(3+log x))dx`
Evaluate : `int "e"^(3"x")/("e"^(3"x") + 1)` dx
The total revenue R = 720 - 3x2 where x is number of items sold. Find x for which total revenue R is increasing.
The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x2). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"`, then the value of k is:
Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`
`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.
The value of `int_((-1)/sqrt(2))^(1/sqrt(2)) (((x + 1)/(x - 1))^2 + ((x - 1)/(x + 1))^2 - 2)^(1/2)`dx is ______.
`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.
Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.
Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
Evaluate: `int_0^π x/(1 + sinx)dx`.
Evaluate `int_0^3root3(x+4)/(root3(x+4)+root3(7-x)) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate:
`int_0^1 |2x + 1|dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 dx`
Evaluate the following integral:
`int_-9^9 x^3/(4-x^2)dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
