Advertisements
Advertisements
Question
Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`
Advertisements
Solution
Let I = `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x)` ...(i)
Using property `int_a^b f(x)dx = int_a^b f(a + b - x)dx`, we get
I = `int_1^3 sqrt(4 - x)/(sqrt(4 - x) + sqrt(x))dx` ...(ii)
On adding equations (i) and (ii}, we get
2I = `int_1^3 (sqrt(x) + sqrt(4 - x))/(sqrt(x) + sqrt(4 - x))dx`
= `int_1^3 1dx`
= `[x]_1^3`
= 3 – 1 = 2
∴ I = 1
APPEARS IN
RELATED QUESTIONS
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
Evaluate`int (1)/(x(3+log x))dx`
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Evaluate : ∫ log (1 + x2) dx
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
`int_"a"^"b" "f"(x) "d"x` = ______
`int_0^{pi/2} log(tanx)dx` = ______
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`
`int_0^1 log(1/x - 1) "dx"` = ______.
`int_0^pi x sin^2x dx` = ______
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
Evaluate:
`int_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`
The value of `int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2)) dx` is
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 ______.
`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.
Evaluate: `int_0^π 1/(5 + 4 cos x)dx`
What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?
`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.
`int_0^(π/2)((root(n)(secx))/(root(n)(secx + root(n)("cosec" x))))dx` is equal to ______.
Evaluate `int_0^3root3(x+4)/(root3(x+4)+root3(7-x)) dx`
Evaluate: `int_-1^1 x^17.cos^4x dx`
Evaluate:
`int_0^1 |2x + 1|dx`
Solve the following.
`int_0^1 e^(x^2) x^3dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/(9x^2 - 1) dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`
