What is the integral from-1 to 1 of (3x^3+xcos(x)+1) ?

The integral from-1 to 1 of (3x^3+xcos(x)+1) is 2

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integral from-1 to 1 of (3x^3+xcos(x)+1)

\int_{- 1}^{1} (3 x^{3} + x cos (x) + 1) d x

2

Solution steps

\int_{- 1}^{1} 3 x^{3} + x cos (x) + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{1} 3 x^{3} d x + \int_{- 1}^{1} x cos (x) d x + \int_{- 1}^{1} 1 d x

\int_{- 1}^{1} 3 x^{3} d x = 0

\int_{- 1}^{1} x cos (x) d x = 0

\int_{- 1}^{1} 1 d x = 2

= 0 + 0 + 2

Simplify

= 2

\int_{1}^{4} ∣ 2 x - 4 ∣ d x

\int_{1}^{2} \frac{1}{x ^{3}} e^{\frac{1}{x}} d x

\int_{2}^{3} 3^{4 x} d x

\int_{0}^{2} (x - 3) (x - 1) d x

\int_{0}^{1} x^{\frac{3}{4}} d x

What is the integral from-1 to 1 of (3x^3+xcos(x)+1) ?
The integral from-1 to 1 of (3x^3+xcos(x)+1) is 2