Advertisements
Advertisements
प्रश्न
Evaluate `int_-1^1 |x^4 - x|dx`.
Advertisements
उत्तर
Let I = `int_-1^1 |x^4 - x|dx`
= `int_-1^0 (x^4 - x)dx - int_0^1 (x^4 - x)dx`
= `[x^5/5 - x^2/2]_-1^0 - [x^5/5 - x^2/2]_0^1`
= `[(0 - 0) - ((-1)/5 - 1/2)] - [(1/5 - 1/2) - 0]`
= `7/10 + 3/10`
= 1.
APPEARS IN
संबंधित प्रश्न
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) -2
(c) 2
(d) ±2
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
By using the properties of the definite integral, evaluate the integral:
`int_((-pi)/2)^(pi/2) sin^2 x dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi log(1+ cos x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
Prove that `int_0^af(x)dx=int_0^af(a-x) dx`
hence evaluate `int_0^(pi/2)sinx/(sinx+cosx) dx`
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
Find `dy/dx, if y = cos^-1 ( sin 5x)`
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
Evaluate: `int_0^pi ("x"sin "x")/(1+ 3cos^2 "x") d"x"`.
`int_0^1 "e"^(2x) "d"x` = ______
Evaluate `int_0^1 x(1 - x)^5 "d"x`
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
Evaluate `int_(-1)^2 "f"(x) "d"x`, where f(x) = |x + 1| + |x| + |x – 1|
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
`int (dx)/(e^x + e^(-x))` is equal to ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
`int_0^(2a)f(x)/(f(x)+f(2a-x)) dx` = ______
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
What is the value of a definite integral when its upper and lower limits are equal?
Which formula is \[P_5\] : Halving the Upper Limit (Addition)?
