=∫_1^3 2x+5dx = ∫_1^32xdx+∫_1^35dx #160; =2.x^2/2 | _1^3 + 5x |_1^3 #160; =(9 1)+(15 5) #160; =8+10 #160; =18 #1 ...

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Integration Using Substitution

Solve: 31∫2...

Question

Solve: $3 \int 1 (2 x + 5) d x$

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Solution

$= \int_{1}^{3} 2 x + 5 d x$

$= \int_{1}^{3} 2 x d x + \int_{1}^{3} 5 d x$

$= 2. \frac{x^{2}}{2}$ ${∣ ∣_{1}^{3} + 5 x ∣ ∣}_{1}^{3}$

$= (9 - 1) + (15 - 5)$

$= 8 + 10$

$= 18$

$∴ \int_{1}^{3} (2 x + 5) d x = 18$

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