Advertisements
Advertisements
प्रश्न
The value of `int_0^(π/4) (sin 2x)dx` is ______.
पर्याय
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
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^(2x) cos^5 xdx`
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` dx is ______.
Evaluate the definite integrals `int_0^pi (x tan x)/(sec x + tan x)dx`
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
`int (cos x + x sin x)/(x(x + cos x))`dx = ?
f(x) = `{:{(x^3/k; 0 ≤ x ≤ 2), (0; "otherwise"):}` is a p.d.f. of X. The value of k is ______
`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______
`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
Evaluate:
`int_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`
`int (dx)/(e^x + e^(-x))` is equal to ______.
If `f(a + b - x) = f(x)`, then `int_0^b x f(x) dx` 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 ______.
`int_0^1|3x - 1|dx` equals ______.
`int_0^(π/4) x. sec^2 x dx` = ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
Evaluate: `int_0^π x/(1 + sinx)dx`.
Evaluate the following definite integral:
`int_1^3 log x dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
