Advertisements
Advertisements
प्रश्न
Find an anti derivative (or integral) of the following function by the method of inspection.
sin 2x
Advertisements
उत्तर
We know that,
`d/dx` cos 2x = - 2 sin 2x
or sin 2x = `-1/2 d/dx` cos 2x
∴ sin 2x = `"d"/"dx" (-1/2 cos 2x)`
Therefore, the antiderivative of sin 2x is `-1/2` cos 2x.
APPEARS IN
संबंधित प्रश्न
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.
e2x
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 (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`int (2 - 3 sinx)/(cos^2 x) dx.`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
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:
`(5x)/((x+1)(x^2 +9))`
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:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
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`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equal
`int (dx)/sqrt(9x - 4x^2)` equals
`int (xdx)/((x - 1)(x - 2))` equals
`int sqrt(1 + x^2) dx` is equal to
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
What is “an integral of \(f\)” ?
Which antiderivative has derivative \(1\)?
Evaluate \[\int \sin x\,dx\]
Evaluate \[\int \text{cosec} x\cot x\,dx\]
Evaluate \[\int \frac{1}{x}\,dx\]
