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
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) cos^2 x dx`
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` dx is ______.
Evaluate the definite integrals `int_0^pi (x tan x)/(sec x + tan x)dx`
Evaluate `int_0^(pi/2) cos^2x/(1+ sinx cosx) dx`
Evaluate = `int (tan x)/(sec x + tan x)` . dx
Find : `int_ (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.
`int_"a"^"b" "f"(x) "d"x` = ______
Choose the correct alternative:
`int_(-9)^9 x^3/(4 - x^2) "d"x` =
f(x) = `{:{(x^3/k; 0 ≤ x ≤ 2), (0; "otherwise"):}` is a p.d.f. of X. The value of k is ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______
`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.
`int_0^1 "e"^(5logx) "d"x` = ______.
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.
The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.
If f(x) = `(2 - xcosx)/(2 + xcosx)` and g(x) = logex, (x > 0) then the value of the integral `int_((-π)/4)^(π/4) "g"("f"(x))"d"x` is ______.
Let `int ((x^6 - 4)dx)/((x^6 + 2)^(1/4).x^4) = (ℓ(x^6 + 2)^m)/x^n + C`, then `n/(ℓm)` is equal to ______.
Evaluate: `int_0^π 1/(5 + 4 cos x)dx`
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.
Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.
Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.
The value of `int_0^(π/4) (sin 2x)dx` is ______.
Evaluate: `int_0^(π/4) log(1 + tanx)dx`.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
`int_-9^9 x^3/(4-x^2) dx` =______
Evaluate:
`int_0^6 |x + 3|dx`
Which property is useful for piecewise functions or modulus (absolute value) functions?
When is \[P_4\] : Special Case of \[P_3\] applied?
