Advertisements
Advertisements
प्रश्न
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
पर्याय
True
False
उत्तर
This statement is True.
Explanation:
Let 4ex – 25 = `A(2e^x - 5) + B d/(dx) (2e^x - 5)`
= 2exA – 5A + B(2ex)
2 × 2ex – 25 = 2ex (A + B) – 5A
∴ A + B = 2
And –25 = –5A
∴ A = 5
5 + B = 2
∴ B = 2 – 5 = – 3.
APPEARS IN
संबंधित प्रश्न
Integrate : sec3 x w. r. t. x.
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x log x.
Integrate the function in x sin-1 x.
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following : `int logx/x.dx`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `sqrt(x^2 + 2x + 5)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Evaluate the following.
∫ x log x dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
`int(logx)^2dx` equals ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`inte^(xloga).e^x dx` is ______
Evaluate:
`int e^(logcosx)dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate the following.
`intx^3e^(x^2) dx`
