Advertisements
Advertisements
प्रश्न
Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`
Advertisements
उत्तर
Let I = `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x)` ...(i)
Using property `int_a^b f(x)dx = int_a^b f(a + b - x)dx`, we get
I = `int_1^3 sqrt(4 - x)/(sqrt(4 - x) + sqrt(x))dx` ...(ii)
On adding equations (i) and (ii}, we get
2I = `int_1^3 (sqrt(x) + sqrt(4 - x))/(sqrt(x) + sqrt(4 - x))dx`
= `int_1^3 1dx`
= `[x]_1^3`
= 3 – 1 = 2
∴ I = 1
APPEARS IN
संबंधित प्रश्न
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_0^2 xsqrt(2 -x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
\[\int\limits_0^k \frac{1}{2 + 8 x^2} dx = \frac{\pi}{16},\] find the value of k.
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Evaluate : `int "e"^(3"x")/("e"^(3"x") + 1)` dx
Evaluate `int_1^3 x^2*log x "d"x`
`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?
`int_0^pi sin^2x.cos^2x dx` = ______
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
If `f(a + b - x) = f(x)`, then `int_0^b x f(x) dx` is equal to
The value of `int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2)) dx` is
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
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.
`int_0^1|3x - 1|dx` equals ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
Evaluate `int_0^(π//4) log (1 + tanx)dx`.
Evaluate `int_-1^1 |x^4 - x|dx`.
Solve the following.
`int_1^3 x^2 logx dx`
If `int_0^1(3x^2 + 2x+a)dx = 0,` then a = ______
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
\[\int_{-2}^{2}\left|x^{2}-x-2\right|\mathrm{d}x=\]
The value of \[\int_{-1}^{1}\left(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right)\mathrm{d}x\] is
