Advertisements
Advertisements
Question
Evaluate: `int_-1^1 x^17.cos^4x dx`
Options
`oo`
1
– 1
0
Solution
0
Explanation:
Let f(x) = x17 cos4x
∴ f(– x) = (– x)17 cos4(– x)
= – x17 cos4x
= – f(x)
`\implies` f(x) is an odd function.
So by the property of definite integration.
`int_-a^a f(x)dx` = 0
If f(x) is an odd function.
`\implies int_-1^1 x^17 cos^4x dx` = 0
APPEARS IN
RELATED QUESTIONS
Evaluate : `intlogx/(1+logx)^2dx`
Evaluate `int_(-2)^2x^2/(1+5^x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) 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^a sqrtx/(sqrtx + sqrt(a-x)) dx`
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` dx is ______.
Evaluate `int_0^(pi/2) cos^2x/(1+ sinx cosx) dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`
`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
`int_0^pi x sin^2x dx` = ______
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0
⇒ `1/4 (square - square)` = 0
⇒ b4 – `square` = 0
⇒ (b2 – a2)(`square` + `square`) = 0
⇒ b2 – `square` = 0 as a2 + b2 ≠ 0
⇒ b = ± `square`
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 ______.
Evaluate `int_-1^1 |x^4 - x|dx`.
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 the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
`int_0^(2a)f(x)/(f(x)+f(2a-x)) dx` = ______
`int_-9^9 x^3/(4-x^2) dx` =______
Evaluate the following definite integral:
`int_-2^3 1/(x + 5) dx`
Evaluate the following integral:
`int_0^1 x (1 - x)^5 dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/(9x^2 - 1) dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
