Question

cual letra es correcta\Calculate the following definite integral ∫_2 ^ 4 (2x ^ 3-7) dx, (Hint: use the fundamental theorem of calculus)

Answer 1

Evaluate the value of definite integral.

$\int ^4_2(2x^3-7)dx=\int ^4_22x^3dx-\int ^4_27dx$$\begin{gathered} \int ^4_22x^3dx-\int ^4_27dx=\lbrack\frac{2x^4}{4}\rbrack^4_2-\lbrack7x\rbrack^4_2 \\ =\frac{1}{2}\lbrack(4)^4-(2)^4\rbrack-7\lbrack4-2\rbrack \\ =\frac{1}{2}\lbrack256-16\rbrack-7\cdot2 \\ =\frac{1}{2}\cdot240-14 \\ =120-14 \\ =106 \end{gathered}$

Answer: 106

Option a is correct.