Advertisements
Advertisements
प्रश्न
Find the following integrals:
`int(1 - x) sqrtx dx`
उत्तर
`int (1 - x) sqrtx dx`
`I = int (x^(1/2) - x^(3/2))` dx
`I= int x^(1/2) dx - int x^(3/2)` dx
`I= 2/3 x^(3/2) - 2/5 x^(5/2) + C`
APPEARS IN
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Evaluate `int tan^(-1) sqrtx dx`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`int (dx)/(sin^2x cos^2x) dx` equals
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`int (dx)/sqrt(9x - 4x^2)` equals
`int (dx)/(x(x^2 + 1))` equals
`f x^2 e^(x^3) dx` equals
`int sqrt(1 + x^2) dx` is equal to
If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.
`d/(dx)x^(logx)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.