What is the integral from-1 to 1 of |x|4^{x^2}ln(4) ?

The integral from-1 to 1 of |x|4^{x^2}ln(4) is 3

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integral from-1 to 1 of |x|4^{x^2}ln(4)

\int_{- 1}^{1} ∣ x ∣ 4^{x^{2}} ln (4) d x

3

Solution steps

\int_{- 1}^{1} ∣ x ∣ \cdot 4^{x^{2}} ln (4) d x

Eliminate Absolutes

= \int_{- 1}^{0} (- x) \cdot 4^{x^{2}} ln (4) d x + \int_{0}^{1} x \cdot 4^{x^{2}} ln (4) d x

\int_{- 1}^{0} (- x) \cdot 4^{x^{2}} ln (4) d x = \frac{3}{2}

\int_{0}^{1} x \cdot 4^{x^{2}} ln (4) d x = \frac{3}{2}

= \frac{3}{2} + \frac{3}{2}

Simplify

\frac{3}{2} + \frac{3}{2} : 3

= 3

What is the integral from-1 to 1 of |x|4^{x^2}ln(4) ?
The integral from-1 to 1 of |x|4^{x^2}ln(4) is 3