Advertisements
Advertisements
प्रश्न
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
Advertisements
उत्तर
We have, `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
Let f(x) = sin|x| + cos|x|
Then, f(x) = f(–x)
Since, f(x) is an even function
So, I = `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
= `2int_0^(π/2) (sinx + cosx)dx`
= `2[-cosx + sinx]_0^(π/2)`
= `2[-cos π/2 + sin π/2 + cos0 - sin0]`
= 2[0 + 1 + 1 – 0]
= 2(2)
= 4
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^pi(xsinx)/(1+sinx)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_(pi/2)^(pi/2) sin^7 x dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x)) "d"x`
Evaluate `int_0^1 x(1 - x)^5 "d"x`
`int_0^{pi/2} log(tanx)dx` = ______
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_0^1 x tan^-1x dx` = ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
`int_0^1 log(1/x - 1) "dx"` = ______.
`int_-1^1x^2/(1+x^2) dx=` ______.
`int_0^pi x*sin x*cos^4x "d"x` = ______.
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.
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)
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
`int_(-5)^5 x^7/(x^4 + 10) dx` = ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
`int_4^9 1/sqrt(x)dx` = ______.
With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.
Evaluate: `int_1^3 sqrt(x + 5)/(sqrt(x + 5) + sqrt(9 - x))dx`
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 integral:
`int_0^1x(1-x)^5dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
Evaluate the following integral:
`int_0^1x(1-x)^5dx`
`int_(pi"/"11)^(9pi"/"22) (dx)/(1 + sqrttan x)` =
