Advertisements
Advertisements
Question
The value of `int_0^(π/4) (sin 2x)dx` is ______.
Options
0
1
`1/2`
`-1/2`
Advertisements
Solution
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
RELATED QUESTIONS
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sqrt(sinx)/(sqrt(sinx) + sqrt(cos x)) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan x))`dx = ?
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/2} cos^2x dx` = ______
`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
`int_0^9 1/(1 + sqrtx)` dx = ______
Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|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.
Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.
`int_0^1|3x - 1|dx` equals ______.
Let f be continuous periodic function with period 3, such that `int_0^3f(x)dx` = 1. Then the value of `int_-4^8f(2x)dx` is ______.
`int_0^(pi/4) (sec^2x)/((1 + tanx)(2 + tanx))dx` equals ______.
Evaluate: `int_0^π 1/(5 + 4 cos x)dx`
What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
`int_1^2 x logx dx`= ______
`int_0^(2a)f(x)/(f(x)+f(2a-x)) dx` = ______
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Solve the following.
`int_0^1e^(x^2)x^3 dx`
Evaluate the following integral:
`int_-9^9 x^3/(4-x^2)dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
\[\int_{-2}^{2}\left|x^{2}-x-2\right|\mathrm{d}x=\]
