Advertisements
Advertisements
प्रश्न
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Advertisements
उत्तर
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 +bb (x + 4)`
= `int_0^2 dx/(-x^2 + x + 1/4 - bb(1/4) + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (bbsqrt17/2)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
APPEARS IN
संबंधित प्रश्न
Integrate the function in `x^2e^x`.
Integrate the function in x log x.
Integrate the function in x (log x)2.
Integrate the function in e2x sin x.
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
`int 1/(4x + 5x^(-11)) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int 1/x "d"x` = ______ + c
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
`int 1/sqrt(x^2 - 9) dx` = ______.
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
`int logx dx = x(1+logx)+c`
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int x sqrt(1 + x^2) dx`
