定積分・広義積分計算機
定積分と広義積分を手順を追って計算する
この計算機は、定積分（すなわち上下限のある積分）を、広義積分も含めて、解法手順を示しながら計算を試みます。
Solution
Your input: calculate $$$\int_{0}^{\frac{\pi}{2}}\left( \theta \sin{\left(2 \right)} \right)d\theta$$$
First, calculate the corresponding indefinite integral: $$$\int{\theta \sin{\left(2 \right)} d \theta}=\frac{\theta^{2} \sin{\left(2 \right)}}{2}$$$ (for steps, see indefinite integral calculator)
According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.
$$$\left(\frac{\theta^{2} \sin{\left(2 \right)}}{2}\right)|_{\left(\theta=\frac{\pi}{2}\right)}=\frac{\pi^{2} \sin{\left(2 \right)}}{8}$$$
$$$\left(\frac{\theta^{2} \sin{\left(2 \right)}}{2}\right)|_{\left(\theta=0\right)}=0$$$
$$$\int_{0}^{\frac{\pi}{2}}\left( \theta \sin{\left(2 \right)} \right)d\theta=\left(\frac{\theta^{2} \sin{\left(2 \right)}}{2}\right)|_{\left(\theta=\frac{\pi}{2}\right)}-\left(\frac{\theta^{2} \sin{\left(2 \right)}}{2}\right)|_{\left(\theta=0\right)}=\frac{\pi^{2} \sin{\left(2 \right)}}{8}$$$
Answer: $$$\int_{0}^{\frac{\pi}{2}}\left( \theta \sin{\left(2 \right)} \right)d\theta=\frac{\pi^{2} \sin{\left(2 \right)}}{8}\approx 1.12180073571225$$$