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Step-by-step Solution

Trigonometric integral $\int_{0}^{\frac{\pi }{4}}\sin\left(4x\right)dx$

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Answer

$0.5$

Step-by-step explanation

Problem to solve:

$\int_0^{\frac{\pi}{4}}sin\left(4x\right)dx$
1

Apply the formula: $\int\sin\left(ax\right)dx$$=-\left(\frac{1}{a}\right)\cos\left(ax\right)$, where $a=4$

$\left[-\frac{1}{4}\cos\left(4x\right)\right]_{0}^{\frac{2}{\sqrt{2}}}$
2

Evaluate the definite integral

$\cos\left(4\cdot 0.7854\right)-0.25-1\cos\left(4\cdot 0\right)-0.25$

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Answer

$0.5$
$\int_0^{\frac{\pi}{4}}sin\left(4x\right)dx$

Main topic:

Integration by substitution

Used formulas:

4. See formulas

Time to solve it:

~ 0.66 seconds