Advertisements
Advertisements
Question
State whether the following statement is True or False:
`int_0^(2"a") "f"(x) "d"x = int_0^"a" "f"(x) "d"x + int_0^"a" "f"("a" - x) "d"x`
Options
True
False
Solution
False
APPEARS IN
RELATED QUESTIONS
Evaluate:
`int_0^1 (1)/sqrt(3 + 2x - x^2)*dx`
Evaluate : `int_0^(pi/2) cosx/((1 + sinx)(2 + sin x))*dx`
Evaluate the following : `int_(-3)^(3) x^3/(9 - x^2)*dx`
Choose the correct option from the given alternatives :
`int_1^2 (1)/x^2 e^(1/x)*dx` =
Evaluate the following : `int_(pi/5)^((3pi)/10) sinx/(sinx + cosx)*dx`
Evaluate the following : `int_0^(pi/2) [2 log (sinx) - log (sin 2x)]*dx`
Evaluate the following definite integrals: If `int_0^"a" (2x + 1)*dx` = 2, find the real value of a.
State whether the following is True or False : `int_4^7 ((11 - x)^2)/((11 - x)^2 + x^2)*dx = (3)/(2)`
Prove that: `int_"a"^"b" "f"(x) "d"x = int_"a"^"c""f"(x) "d"x + int_"c"^"b" "f"(x) "d"x`, where a < c < b
Evaluate `int_1^"e" 1/(x(1 + log x)^2) "d"x`
Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2)) "d"x`
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_(-2)^2 sqrt((2 - x)/(2 + x))` = ?
`int_0^(pi/2) root(7)(sin x)/(root(7)(sin x) + root(7)(cos x))`dx = ?
Solve the following `int_1^3 x^2log x dx`
Evaluate the following definite integral:
`int_4^9 1/sqrtx dx`
Evaluate the following definite intergral:
`int_1^3 log xdx`
Evaluate the following integral:
`int_0^1 x(1-x)^5dx`
Evaluate the following definite intergral:
`int_4^9 1/sqrt(x)dx`
Solve the following.
`int_1^3x^2log x dx`
