Advertisements
Advertisements
प्रश्न
Find the following integrals:
`int(1 - x) sqrtx dx`
Advertisements
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).`
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
Find the following integrals:
`int(sec^2x)/(cosec^2x) 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:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
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/sqrt(sin^3 x sin(x + alpha))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`int (dx)/(sin^2x cos^2x) dx` equals
`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
`int x^2 e^(x^3) dx` equals
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
What is anti derivative of `e^(2x)`
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 ______.
