Advertisements
Advertisements
Question
Verify the following:
`int (2x + 3)/(x^2 + 3x) "d"x = log|x^2 + 3x| + "C"`
Advertisements
Solution
L.H.S. = `int (2x + 3)/(x^2 + 3x) "d"x`
Put x2 + 3x = t
∴ (2x + 3) dx = dt
⇒ `int "dt"/"t" = log |"t"|`
⇒ `log |x^2 + 3x| + "C"` = R.H.S.
L.H.S. = R.H.S.
Hence verified.
APPEARS IN
RELATED QUESTIONS
If f is an integrable function, show that
If \[I_{10} = \int\limits_0^{\pi/2} x^{10} \sin x\ dx,\] then the value of I10 + 90I8 is
\[\int\limits_0^{2a} f\left( x \right) dx\] is equal to
The value of \[\int\limits_0^{\pi/2} \log\left( \frac{4 + 3 \sin x}{4 + 3 \cos x} \right) dx\] is
Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .
\[\int\limits_0^1 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) dx\]
\[\int\limits_0^{\pi/3} \frac{\cos x}{3 + 4 \sin x} dx\]
\[\int\limits_1^2 \frac{x + 3}{x\left( x + 2 \right)} dx\]
\[\int\limits_{- \pi/2}^{\pi/2} \sin^9 x dx\]
\[\int\limits_0^{15} \left[ x^2 \right] dx\]
\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
Using second fundamental theorem, evaluate the following:
`int_0^(pi/2) sqrt(1 + cos x) "d"x`
Using second fundamental theorem, evaluate the following:
`int_1^2 (x - 1)/x^2 "d"x`
Choose the correct alternative:
The value of `int_(- pi/2)^(pi/2) cos x "d"x` is
Choose the correct alternative:
`Γ(3/2)`
Evaluate `int (x^2 + x)/(x^4 - 9) "d"x`
If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.
