Advertisements
Advertisements
Question
State whether the following is True or False : `int_1^2 sqrt(x)/(sqrt(3 - x) + sqrt(x))*dx = (1)/(2)`
Options
True
False
Solution
`int_"a"^"b" f(x)/(f(x) + f("a" + "b" - x))*dx`
= `(1)/(2)("b" - "a")`
Here, f(x) = `sqrt(x)`, a = 1, b = 2 True.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_1^9(x + 1)/sqrt(x)*dx`
Evaluate the following : `int_0^1 t^2 sqrt(1 - t)*dt`
Evaluate the following : `int_0^pi x sin x cos^2x*dx`
Evaluate the following : `int_0^1 (1/(1 + x^2))sin^-1((2x)/(1 + x^2))*dx`
Evaluate the following : `int_(pi/5)^((3pi)/10) sinx/(sinx + cosx)*dx`
Evaluate the following definite integrals: `int_1^2 dx/(x^2 + 6x + 5)`
Solve the following : `int_2^3 x/(x^2 - 1)*dx`
Solve the following : `int_1^2 (5x^2)/(x^2 + 4x + 3)*dx`
Prove that: `int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x) "d"x`
State whether the following statement is True or False:
`int_0^1 1/(2x + 5) "d"x = log(7/5)`
By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Solution: Let I = `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`
∴ x + 3 = A(x + 2) + B.x
∴ A = `square`, B = `square`
∴ I = `int_1^2[("( )")/x + ("( )")/((x + 2))] "d"x`
∴ I = `[square log x + square log(x + 2)]_1^2`
∴ I = `square`
`int_0^(pi/2) (cos x)/((4 + sin x)(3 + sin x))`dx = ?
Evaluate the following definite integrals:
`int _1^2 (3x) / ( (9 x^2 - 1)) * dx`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5) dx`
Evaluate the following integrals:
`int_-9^9 (x^3)/(4 - x^2) dx`
`int_a^b f(x) dx = int_a^b f (t) dt`
Solve the following:
`int_0^1e^(x^2)x^3dx`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5) · dx`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5).dx`
Solve the following.
`int_1^3x^2 logx dx`
