Advertisements
Advertisements
प्रश्न
Evaluate the definite integral:
`int_0^pi (sin^2 x/2 - cos^2 x/2) dx`
Advertisements
उत्तर
∴ `int_0^pi (sin^2 x/2 - cos^2 x/2) dx ...(because cos^2 x/2 - sin^2 x = cos x)`
`= -int_0^pi cos x dx = - [sin x]_0^pi`
`= - (sin pi - sin 0)`
`= [0 - 0] = 0`
APPEARS IN
संबंधित प्रश्न
If `int_0^h1/(2+8x^2)dx=pi/16 `then find the value of h.
Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)dx`
Evaluate the definite integral:
`int_(-1)^1 (x + 1)dx`
Evaluate the definite integral:
`int_2^3 1/x dx`
Evaluate the definite integral:
`int_1^2 (4x^3 - 5x^2 + 6x + 9) dx`
Evaluate the definite integral:
`int_0^(pi/4) sin2xdx`
Evaluate the definite integral:
`int_0^(pi/2) cos 2x dx`
Evaluate the definite integral:
`int_4^5 e^x dx`
Evaluate the definite integral:
`int_0^(pi/4) tan x dx`
Evaluate the definite integral:
`int_(pi/6)^(pi/4) cosec x dx`
Evaluate the definite integral:
`int_0^1 dx/(1+x^2)`
Evaluate the definite integral:
`int_2^3 dx/(x^2 - 1)`
Evaluate the definite integral:
`int_0^(pi/2) cos^2 xdx`
Evaluate the definite integral:
`int_0^1 x e^(x^2) dx`
Evaluate the definite integral:
`int_1^2 (5x^2)/(x^2 + 4x + 3)`
Evaluate the definite integral:
`int_0^(pi/4) (2 sec^2 x + x^3 + 2) dx`
Evaluate the definite integral:
`int_0^1 (xe^x + sin (pix)/4)`
`int_1^(sqrt3)dx/(1+x^2) ` equals:
`int_6^(2/3) (dx)/(4 + 9x^2)` equals
Evaluate:
`int_0^π(sin^4x + cos^4x)dx`
Hence evaluate:
`int_(-2π)^(2π) (sin^4x + cos^4x)/(1 + e^x)dx`
What does the Fundamental Theorem of Integral Calculus connect?
If \(f\) is continuous on an interval, which expression defines the area function?
Which expression correctly applies the limits to a definite integral?
For \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx,\] which substitution is used?
Under the substitution \[30-x^{\frac32}=t,\] what is the correct expression for \(\sqrt{x}\,dx\)?
An antiderivative of \[\frac{\sqrt{x}}{(30-x^{\frac32})^2}\] is:
For \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt,\] which substitution and differential relation are correct?
