Exercise
$\int_0^{\frac{\pi}{3}}\left(\:3\sin\left(2t\right)i\right)dt$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function 3sin(2t)i from 0 to pi/3. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the formula: \int\sin\left(ax\right)dx=-\left(\frac{1}{a}\right)\cos\left(ax\right)+C, where a=2 and x=t. Multiply the fraction and term in - \left(\frac{1}{2}\right)\cos\left(2t\right).
Integrate the function 3sin(2t)i from 0 to pi/3
Final answer to the exercise
$-\frac{3}{2}\cos\left(\frac{2\pi }{3}\right)i+\frac{3}{2}i$