Question

I need to know the answer of the following image

Answer 1

Answer: Area = 2.

Explanation:

You can set up an integral with boundaries -1 and 1 and the f(x) equation to solve this.

`\int\limits^1_- {3x^2 + 4x} \, dx`

Then simplify using the sum rule and solve each part of the equation to get the area:

`\int\limits^1_- {3x^2 + 4x} \, dx = \int\limits^1_- {3x^2} \, dx + \int\limits^1_- {4x} \, dx`

`\int\limits^1_- {3x^2} \, dx = 3 \int\limits^1_- {x^2} \, dx = 3 ((x^3)/(3)) = x^3 = (1)^3-(-1)^3 = 2`

`\int\limits^1_- {4x} \, dx = 4\int\limits^1_- {x} \, dx = 4((x^2)/(2) ) = 2x^2 = 2(1)^2 - 2(-1)^2 = 0`

Add the solutions together to get: 2 + 0 = 2, Area = 2.