Advertisements
Advertisements
प्रश्न
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Advertisements
उत्तर
`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
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int(1 - x) sqrtx dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
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:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/sqrt(9x - 4x^2)` equal
`int e^x sec x(1 + tanx) dx` equals
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
