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Definite Integration (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Definite Integration (p-1)2 Marks
Question
Evaluate the following definite integrals : $\int_1^3 \log x d x$
✓

Answer

$
\begin{aligned}
& \int_1^3 \log x d x=\int_1^3(\log x) \cdot 1 d x \\
= & {\left.[(\log x)] \int 1 d x\right]_1^3-\int_1^3\left[\frac{d}{d x}(\log x) \int 1 d x\right] d x } \\
= & {[(\log x) x]_1^3-\int_1^3 \frac{1}{x} \times x d x } \\
= & (3 \log 3-\log 1)-\int_1^3 1 d x \\
= & 3 \log 3-[x]_1^3 \\
= & \log 3^3-(3-1) \\
= & \log 27-2 .
\end{aligned}
$

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