Advertisements
Advertisements
Question
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Solution
`f(x) =∫_0^x t sin t dt`
We know that integration is the inverse process of differentiation.
`∴ f ' (x) = d/dx[∫_0^xtsintdt] = x sinx`
APPEARS IN
RELATED QUESTIONS
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`sqrt((1-sqrtx)/(1+sqrtx))`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (xdx)/((x - 1)(x - 2))` equals
`int sqrt(x^2 - 8x + 7) 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)` = ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
