Kalkulator Integral Tentu dan Tak Wajar

Kalkulator akan mencoba mengevaluasi integral tentu (yaitu dengan batas-batas), termasuk integral tak wajar, dengan menampilkan langkah-langkahnya.

Enter a function:

Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: calculate $$$\int_{t^{2}}^{t}\left( \frac{\sin{\left(x \right)}}{x} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{\sin{\left(x \right)}}{x} d x}=\operatorname{Si}{\left(x \right)}$$$ (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.

$$$\left(\operatorname{Si}{\left(x \right)}\right)|_{\left(x=t\right)}=\operatorname{Si}{\left(t \right)}$$$

$$$\left(\operatorname{Si}{\left(x \right)}\right)|_{\left(x=t^{2}\right)}=\operatorname{Si}{\left(t^{2} \right)}$$$

$$$\int_{t^{2}}^{t}\left( \frac{\sin{\left(x \right)}}{x} \right)dx=\left(\operatorname{Si}{\left(x \right)}\right)|_{\left(x=t\right)}-\left(\operatorname{Si}{\left(x \right)}\right)|_{\left(x=t^{2}\right)}=\operatorname{Si}{\left(t \right)} - \operatorname{Si}{\left(t^{2} \right)}$$$

Answer: $$$\int_{t^{2}}^{t}\left( \frac{\sin{\left(x \right)}}{x} \right)dx=\operatorname{Si}{\left(t \right)} - \operatorname{Si}{\left(t^{2} \right)}$$$

Please try a new game Rotatly

Kalkulator Integral Tentu dan Tak Wajar

Hitung integral tentu dan tak wajar langkah demi langkah

Solution