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 $$$\int_{0}^{\frac{2}{3}}\left( \cos^{2}{\left(x \right)} - \cos^{2}{\left(2 x \right)} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\left(\cos^{2}{\left(x \right)} - \cos^{2}{\left(2 x \right)}\right)d x}=\sin^{3}{\left(x \right)} \cos{\left(x \right)}$$$ (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.

$$$\left(\sin^{3}{\left(x \right)} \cos{\left(x \right)}\right)|_{\left(x=\frac{2}{3}\right)}=\sin^{3}{\left(\frac{2}{3} \right)} \cos{\left(\frac{2}{3} \right)}$$$

$$$\left(\sin^{3}{\left(x \right)} \cos{\left(x \right)}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{\frac{2}{3}}\left( \cos^{2}{\left(x \right)} - \cos^{2}{\left(2 x \right)} \right)dx=\left(\sin^{3}{\left(x \right)} \cos{\left(x \right)}\right)|_{\left(x=\frac{2}{3}\right)}-\left(\sin^{3}{\left(x \right)} \cos{\left(x \right)}\right)|_{\left(x=0\right)}=\sin^{3}{\left(\frac{2}{3} \right)} \cos{\left(\frac{2}{3} \right)}$$$

Answer: $$$\int_{0}^{\frac{2}{3}}\left( \cos^{2}{\left(x \right)} - \cos^{2}{\left(2 x \right)} \right)dx=\sin^{3}{\left(\frac{2}{3} \right)} \cos{\left(\frac{2}{3} \right)}\approx 0.185825397011352$$$

Please try a new game Rotatly

Kalkulator Integral Tentu dan Tak Wajar

Hitung integral tentu dan tak wajar langkah demi langkah

Solution