Advertisements
Advertisements
प्रश्न
The value of `int_0^(π/4) (sin 2x)dx` is ______.
विकल्प
0
1
`1/2`
`-1/2`
Advertisements
उत्तर
The value of `int_0^(π/4) (sin 2x)dx` is `underlinebb(1/2)`.
Explanation:
`int_0^(π/4) (sin 2x)dx`
Let u = 2x
If x = 0 then, u = 0
and x = `π/4` then u = `π/2`.
`\implies` du = 2 dx
`1/2 int_0^(π/2) sin u du = -1/2 [cos u]_0^(π/2)`
= `-1/2 [0 - 1]`
= `1/2`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intlogx/(1+logx)^2dx`
Evaluate: `int_(-a)^asqrt((a-x)/(a+x)) dx`
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
Evaluate: `int_1^4 {|x -1|+|x - 2|+|x - 4|}dx`
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
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"`
Find : `int_ (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.
Evaluate `int_0^1 x(1 - x)^5 "d"x`
The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on ______.
`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`int_-9^9 x^3/(4 - x^2)` dx = ______
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_0^1 log(1/x - 1) "dx"` = ______.
`int_-1^1x^2/(1+x^2) dx=` ______.
`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_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`
`int (dx)/(e^x + e^(-x))` is equal to ______.
Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`
If `int_0^1(sqrt(2x) - sqrt(2x - x^2))dx = int_0^1(1 - sqrt(1 - y^2) - y^2/2)dy + int_1^2(2 - y^2/2)dy` + I then I equal.
The integral `int_0^2||x - 1| -x|dx` is equal to ______.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k 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 ______.
With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Solve the following.
`int_1^3 x^2 logx dx`
Evaluate `int_0^3root3(x+4)/(root3(x+4)+root3(7-x)) dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
