Advertisements
Advertisements
प्रश्न
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is ______.
पर्याय
–1
0
1
2
Advertisements
उत्तर
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is 0.
Explanation:
f(x) = `e^(cos^2x) sin^3 (2n + 1)x`
f(–x) = `e^(cos^2(-x)) sin^3 (2n + 1)(-x)`
f(–x) = `-e^(cos^2x) sin^3 (2n + 1)x`
∵ f(–x) = –f(x)
So, `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` = 0
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)dx`
Show that `int_0^a f(x)g (x)dx = 2 int_0^a f(x) dx` if f and g are defined as f(x) = f(a-x) and g(x) + g(a-x) = 4.
Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`
Evaluate : ∫ log (1 + x2) dx
Evaluate `int_1^3 x^2*log x "d"x`
`int_0^{pi/2} xsinx dx` = ______
`int_0^{pi/2} cos^2x dx` = ______
`int_0^pi sin^2x.cos^2x dx` = ______
`int_0^1 "e"^(5logx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
Evaluate the following:
`int_0^(pi/2) "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos4x)
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
Evaluate: `int_(-1)^3 |x^3 - x|dx`
`int_4^9 1/sqrt(x)dx` = ______.
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 ______.
Evaluate: `int_1^3 sqrt(x + 5)/(sqrt(x + 5) + sqrt(9 - x))dx`
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
Evaluate the following integral:
`int_0^1 x(1 - 5)^5`dx
If `int_0^1(3x^2 + 2x+a)dx = 0,` then a = ______
Solve the following.
`int_0^1e^(x^2)x^3 dx`
Solve the following.
`int_0^1 e^(x^2) x^3dx`
Evaluate the following integral:
`int_0^1x(1-x)^5dx`
