Advertisements
Advertisements
प्रश्न
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
विकल्प
`8/pi`
`4/pi`
`2/pi`
`1/pi`
उत्तर
`int_(-2)^2 |x cos pix| "d"x` is equal to `8/pi`.
Explanation:
Since I = `int_(-2)^2 |x cos pix| "d"x`
= `2 int_0^2 |x cos pix| "d"x`
= `2 {int_0^(1/2) |x cos pix|"d"x + int_(1/2)^(3/2) |x cos pix| "d"x + int_(3/2)^2 |x cos pix| "d"x}`
= `8/pi`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsec^nxtanxdx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) cos^2 x dx`
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_0^pi log(1+ cos x) dx`
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`int_0^{pi/2} xsinx dx` = ______
`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.
`int_0^1 (1 - x)^5`dx = ______.
If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)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_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
Let f be a real valued continuous function on [0, 1] and f(x) = `x + int_0^1 (x - t)f(t)dt`. Then, which of the following points (x, y) lies on the curve y = f(x)?
The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
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`.
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is ______.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
Evaluate the following definite integral:
`int_-2^3 1/(x + 5) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
