Advertisements
Advertisements
Question
Evaluate the following definite integrals: if `int_1^"a" (3x^2 + 2x + 1)*dx` = 11, find a.
Solution
Given, `int_1^"a" (3x^2 + 2x + 1)*dx` = 11
∴ `[(3x^3)/3+ (2x^2)/2 + x]_1^"a"` = 11
∴ `[x^3 + x^2 + x]_1^"a"` = 11
∴ (a3 + a2 + a) – (1 + 1 + 1) = 11
∴ a3 + a2 + a – 3 = 11
∴ a3 + a2 + a – 14 = 0
∴ (a – 2)(a2 + 3a + 7) = 0
∴ a = 2 or a2 + 3a + 7 = 0
But a2 + 3a + 7 = 0 does not have eal roots.
∴ a = 2.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^4 (1)/sqrt(4x - x^2)*dx`
Evaluate:
`int_0^(pi/2) sqrt(cos x) sin^3x * dx`
Evaluate : `int_0^(pi/2) (1)/(5 + 4 cos x)*dx`
Evaluate the following:
`int_0^(pi/2) log(tanx)dx`
Evaluate the following : `int_((-pi)/4)^(pi/4) x^3 sin^4x*dx`
Evaluate the following : `int_0^1 (logx)/sqrt(1 - x^2)*dx`
Choose the correct option from the given alternatives :
`int_0^(pi/2) sn^6x cos^2x*dx` =
Evaluate the following : `int_0^pi x*sinx*cos^4x*dx`
Solve the following : `int_(-2)^3 (1)/(x + 5)*dx`
Prove that: `int_0^(2"a") "f"(x) "d"x = int_0^"a" "f"(x) "d"x + int_0^"a" "f"(2"a" - x) "d"x`
Choose the correct alternative:
`int_(-2)^3 1/(x + 5) "d"x` =
`int_(-2)^2 sqrt((2 - x)/(2 + x))` = ?
Evaluate the following definite integrals: `int_-2^3 1/(x + 5) *dx`
`int_0^1 1/(2x + 5)dx` = ______
`int_0^(π/2) (sin^2 x.dx)/(1 + cosx)^2` = ______.
Evaluate the following definite intergral:
`int_1^2 (3x)/((9x^2-1 )`dx
Evaluate the following definite integral:
`int_4^9 1/sqrtx dx`
Evaluate the following definite integral:
`int_1^2 (3x)/((9x^2 - 1))*dx`
Evaluate the following definite intergral.
`int_1^2 (3x)/((9x^2 - 1))dx`
