Question

Evaluate the integral as limit of a sum: $\int\limits^2_0 {(3x^{2}-1)} \, dx$

Answer 1

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Answer 2

Answer:

6

Step-by-step explanation:

We have to find integration of $(3x^2 - 1)$ w. r. t. x

$\int\limits^2_0 {(3x^2 -1)} \, dx \\= \int\limits^2_0 {3x^2} \, dx -\int\limits^2_0 {1} \, dx \\\\=[\dfrac {3x^3}3 ]^2_0\ -[x]^2_0\\=[x^3]^2_0 -[x]^2_0$

Now we will apply the limit in

$[\dfrac {3x^3}3 ]^2_0\ -[x]^2_0$

$=[2^3 - 0] - [2 - 0]\\=8 - 2\\=6$

Therefore the answer is 6.

$\int\limits^2_0 {(3x^2 -1)} \, dx$ = 6