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2 ∫ 1 X √ 3 X − 2 D X - Mathematics

Sum

\[\int\limits_1^2 x\sqrt{3x - 2} dx\]

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Solution

\[\int_1^2 x\sqrt{3x - 2} d x\]

\[Let, 3x - 2 = t,\text{ then }3dx = dt\]

\[\text{when, }x = 1 ; t = 1\text{ and }x = 2 ; t = 4\]

\[\text{Therefore the integral becomes}\]

\[ \int_1^4 \frac{t + 2}{3}\sqrt{t} \frac{dt}{3}\]

\[ = \frac{1}{9} \int_1^4 t^\frac{3}{2} + 2\sqrt{t} dt\]

\[ = \frac{1}{9} \left[ \frac{2 t^\frac{5}{2}}{5} + \frac{4 t^\frac{3}{2}}{3} \right]_1^4 \]

\[ = \frac{1}{9}\left[ \frac{64}{5} + \frac{32}{3} - \frac{2}{5} - \frac{4}{3} \right]\]

\[ = \frac{46}{135}\]

Concept: Definite Integrals Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 20 Definite Integrals
Revision Exercise | Q 2 | Page 121
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