Advertisements
Advertisements
Question
Evaluate `int_-1^1 |x^4 - x|dx`.
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate : `intlogx/(1+logx)^2dx`
Evaluate : `intsec^nxtanxdx`
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)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/2) (sin x - cos x)/(1+sinx cos x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
Evaluate : `int "e"^(3"x")/("e"^(3"x") + 1)` dx
Evaluate: `int_0^pi ("x"sin "x")/(1+ 3cos^2 "x") d"x"`.
`int_1^2 1/(2x + 3) dx` = ______
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
`int (cos x + x sin x)/(x(x + cos x))`dx = ?
`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan x))`dx = ?
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
f(x) = `{:{(x^3/k; 0 ≤ x ≤ 2), (0; "otherwise"):}` is a p.d.f. of X. The value of k is ______
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
Show that `int_0^(pi/2) (sin^2x)/(sinx + cosx) = 1/sqrt(2) log (sqrt(2) + 1)`
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
Evaluate the following:
`int_0^(pi/2) "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos4x)
If `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`, then the value of k is:
`int_4^9 1/sqrt(x)dx` = ______.
Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.
If `int_0^1(3x^2 + 2x+a)dx = 0,` then a = ______
Solve the following.
`int_0^1e^(x^2)x^3 dx`
Evaluate the following integrals:
`int_-9^9 x^3/(4 - x^3 ) dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`
