Mathematics

Evaluate:$$ \int _{ 1 }^{ 3 }(x^2+4)dx$$.


SOLUTION
$$\int^{3}_{1}{\left( {x}^{2} + 4 \right) dx}$$
$$= \int^{3}_{1}{{x}^{2} \; dx} + 4 \int^{3}_{1}{dx}$$
$$= \left[ \cfrac{{x}^{3}}{3} + 4x \right]_{1}^{3}$$
$$= \left( \cfrac{{3}^{3}}{3} + 4 \times 3 \right) - \left( \cfrac{{1}^{3}}{3} + 4 \times 1 \right)$$
$$= \left( 9 + 12 \right) - \left( \cfrac{1}{3} + 4 \right)$$
$$= 21 - \cfrac{13}{3}$$
$$= \cfrac{63 - 13}{3}$$
$$= \cfrac{50}{3}$$
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Subjective Medium Published on 17th 09, 2020
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