Mathematics

Evaluate using limit of sum:
$$\displaystyle \int_{1}^{3} {(x+1)^2}dx$$


ANSWER

$$28$$


SOLUTION

$$\displaystyle \int_{1}^{3} {(x+1)^2}dx$$

Let $$t=(x+1)\implies dt=dx$$

$$ x \to 1\to 3$$ 

$$ t\to 2 \to 4$$

$$\displaystyle \int _2^4 t^2 dt $$ 

$$\left.\dfrac {t^3}3\right]_2^4$$ 

$$\dfrac{4^3}{2}-\dfrac {2^3}{2}$$ 

$$32-4=28$$

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Single Correct Medium Published on 17th 09, 2020
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