Mathematics

$$\displaystyle \int_2^4 (6x^3 + 5x)  dx =$$


SOLUTION
$$\displaystyle I = \int_z^y (6x^3 + 5x)dx$$
$$\displaystyle =6\int_z^y x^3dx + 5\int_z^y x \, dx$$
$$=6\left[\dfrac{x^4}{4}\right]^y_z + 5\left[\dfrac{x^2}{2}\right]^y_z$$
$$=\dfrac{3}{2} \left[y^4 - z^4\right] + \dfrac{3}{2} [y^2 - z^2] = \dfrac{3}{2}[240] + \dfrac{5}{2}[12]$$
$$=360+30 = 390$$
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Subjective Medium Published on 17th 09, 2020
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