Test Index

Integral Calculus

© examsnet.com

Question : 61 of 73

Marks: +1, -0

Evaluate the value of

\int\limits_{0}^{3}(3 x^{2}+5 x+2) d x

55
57
55.5
56

Solution:

Concept:

Definite integral evaluation using the fundamental theorem of calculus.

Explanation:

Find the antiderivative

F(x) = \int (3x^2 + 5x + 2) \, dx

.

F(x) = x^3 + \frac{5}{2}x^2 + 2x + C

.

Evaluate

F(3) - F(0)

:

F(3) = 3^3 + \frac{5}{2} \cdot 3^2 + 2 \cdot 3 = 27 + \frac{45}{2} + 6 = 33 + 22.5 = 55.5

.

F(0) = 0

.

Thus, the integral equals

55.5

.

Answer:

55.5

© examsnet.com

Go to Question:

Prev Question

Next Question