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.

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Solution

Your input: calculate $$$\int_{0}^{\frac{\pi}{2}}\left( \cos^{4}{\left(x \right)} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\cos^{4}{\left(x \right)} d x}=\frac{12 x + 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32}$$$ (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.

$$$\left(\frac{12 x + 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32}\right)|_{\left(x=\frac{\pi}{2}\right)}=\frac{3 \pi}{16}$$$

$$$\left(\frac{12 x + 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{\frac{\pi}{2}}\left( \cos^{4}{\left(x \right)} \right)dx=\left(\frac{12 x + 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32}\right)|_{\left(x=\frac{\pi}{2}\right)}-\left(\frac{12 x + 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32}\right)|_{\left(x=0\right)}=\frac{3 \pi}{16}$$$

Answer: $$$\int_{0}^{\frac{\pi}{2}}\left( \cos^{4}{\left(x \right)} \right)dx=\frac{3 \pi}{16}\approx 0.589048622548086$$$

Kalkulator Integral Tentu dan Tak Wajar

Hitung integral tentu dan tak wajar langkah demi langkah

Solution