Advertisements
Advertisements
Question
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
Advertisements
Solution
We have I = `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x` .....(1)
= `int_2^8 sqrt(10 - (10 - x))/(sqrt(10 - x) + sqrt(10 - (10 - x)) "d"x` .....By (P3)
⇒ I = `int_2^8 sqrt(x)/(sqrt(10 - x) + sqrt(x)) "d"x` ....(2)
Adding (1) and (2), we get
2I = `int_2^8 1"d"x = 8 - ` = 6
Hence I = 3
APPEARS IN
RELATED QUESTIONS
Evaluate : `int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`
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^(pi/2) (2log sin x - log sin 2x)dx`
Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Evaluate : `int "x"^2/("x"^4 + 5"x"^2 + 6) "dx"`
Find `dy/dx, if y = cos^-1 ( sin 5x)`
`int_2^4 x/(x^2 + 1) "d"x` = ______
Evaluate `int_1^3 x^2*log x "d"x`
`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?
`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______
`int_0^{pi/2} log(tanx)dx` = ______
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
`int_0^pi x sin^2x dx` = ______
`int_0^9 1/(1 + sqrtx)` dx = ______
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
`int (dx)/(e^x + e^(-x))` is equal to ______.
`int_(-5)^5 x^7/(x^4 + 10) dx` = ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`
`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.
If `int_0^1(sqrt(2x) - sqrt(2x - x^2))dx = int_0^1(1 - sqrt(1 - y^2) - y^2/2)dy + int_1^2(2 - y^2/2)dy` + I then I equal.
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 ______.
The value of `int_((-1)/sqrt(2))^(1/sqrt(2)) (((x + 1)/(x - 1))^2 + ((x - 1)/(x + 1))^2 - 2)^(1/2)`dx is ______.
The integral `int_0^2||x - 1| -x|dx` is equal to ______.
`int_0^1|3x - 1|dx` equals ______.
`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
The value of `int_0^(π/4) (sin 2x)dx` is ______.
Evaluate: `int_0^π x/(1 + sinx)dx`.
Evaluate the following integral:
`int_0^1 x(1 - 5)^5`dx
Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
