Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[Let\ I = \int_1^e \frac{\log x}{x} d x\]
\[Let\ \log x = u\]
\[ \Rightarrow \frac{1}{x} dx = du\]
\[ \therefore I = \int u\ d u\]
\[ \Rightarrow I = \left[ \frac{u^2}{2} \right]\]
\[ \Rightarrow I = \left[ \frac{(\log x )^2}{2} \right]_1^e \]
\[ \Rightarrow I = \frac{1}{2} - 0\]
\[ \Rightarrow I = \frac{1}{2}\]
APPEARS IN
संबंधित प्रश्न
If \[\int\limits_0^1 \left( 3 x^2 + 2x + k \right) dx = 0,\] find the value of k.
Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .
`int_0^(2a)f(x)dx`
\[\int\limits_0^1 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) dx\]
\[\int\limits_0^1 \frac{1 - x}{1 + x} dx\]
\[\int\limits_0^{15} \left[ x^2 \right] dx\]
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
Evaluate the following:
Γ(4)
Evaluate the following:
`Γ (9/2)`
Choose the correct alternative:
`int_0^oo "e"^(-2x) "d"x` is
If `intx^3/sqrt(1 + x^2) "d"x = "a"(1 + x^2)^(3/2) + "b"sqrt(1 + x^2) + "C"`, then ______.
What is the meaning of a definite integral?
Evaluate \[\int_{1}^{3}(2x+1)\,dx\].
If velocity changes with time, what does a definite integral give over a time interval?
