Advertisements
Advertisements
प्रश्न
Evaluate:
`int_0^1 (1)/sqrt(3 + 2x - x^2)*dx`
उत्तर
`int_0^1 (1)/sqrt(3 + 2x - x^2)*dx`
= `int_0^1 (1)/sqrt(3 - (x^2 - 2x + 1) + 1)*dx`
= `int_0^1 (1)/sqrt((2)^2 - (x - 1)^2)*dx`
= `[sin^-1 ((x - 1)/2)]_0^1`
= `sin^-1(0) - sin^-1(-1/2)`
= `0 - sin^-1 (-sin pi/6)`
= `-sin^-1[sin(- pi/6)]`
= `-(- pi/6)`
= `pi/(6)`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_1^9(x + 1)/sqrt(x)*dx`
Evaluate : `int_0^1 x tan^-1x*dx`
Evaluate : `int_0^(pi/4) (sec^2x)/(3tan^2x + 4tan x +1)*dx`
Evaluate : `int_(-1)^1 (1)/(a^2e^x + b^2e^(-x))*dx`
Evaluate : `int_0^pi (1)/(3 + 2sinx + cosx)*dx`
Evaluate : `int_1^3 (cos(logx))/x*dx`
Evaluate the following : `int_0^3 x^2(3 - x)^(5/2)*dx`
Evaluate the following : `int_((-pi)/4)^(pi/4) (x + pi/4)/(2 - cos 2x)*dx`
Choose the correct option from the given alternatives :
`int_1^2 (1)/x^2 e^(1/x)*dx` =
Choose the correct option from the given alternatives :
Let I1 = `int_e^(e^2) dx/logx "and" "I"_2 = int_1^2 e^x/x*dx`, then
Evaluate the following : `int_0^1 1/(1 + sqrt(x))*dx`
Evaluate the following : `int_0^pi x*sinx*cos^4x*dx`
Evaluate the following : `int_0^1 (1/(1 + x^2))sin^-1((2x)/(1 + x^2))*dx`
Evaluate the following : `int_0^(pi/2) 1/(6 - cosx)*dx`
Evaluate the following : `int_(-2)^(3) |x - 2|*dx`
Evaluate the following integrals : `int_0^"a" x^2("a" - x)^(3/2)*dx`
Choose the correct alternative :
`int_2^3 x/(x^2 - 1)*dx` =
Fill in the blank : `int_0^2 e^x*dx` = ________
State whether the following is True or False : `int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx = (9)/(2)`
Solve the following : `int_2^3 x/((x + 2)(x + 3))*dx`
Solve the following : `int_(-4)^(-1) (1)/x*dx`
Choose the correct alternative:
`int_2^3 x^4 "d"x` =
`int_1^2 x^2 "d"x` = ______
State whether the following statement is True or False:
`int_2^3 x/(x^2 + 1) "d"x = 1/2 log 2`
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`
Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2)) "d"x`
`int_0^(pi/2) (cos x)/((4 + sin x)(3 + sin x))`dx = ?
`int_(-5)^5 log ((7 - x)/(7 + x))`dx = ?
`int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2))` dx = ?
Evaluate the following definite integrats:
`int_4^9 1/sqrt x dx`
Solve the following.
`int_1^3 x^2 logx dx`
Evaluate the following definite integral:
`int_1^2 (3x)/((9x^2 - 1))dx`
Evaluate the following definite intergral:
`int_1^3 log xdx`
`int_0^1 1/(2x + 5)dx` = ______
Evaluate the following integrals:
`int_-9^9 (x^3)/(4 - x^2) dx`
Evaluate the following definite intergral:
`int _1^3logxdx`
Solve the following.
`int_1^3 x^2 log x dx `
