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 $$$\int_{0}^{1}\left( \sqrt{t^{6}} \right)dt=\int_{0}^{1}\left( t^{3} \right)dt$$$

First, calculate the corresponding indefinite integral: $$$\int{t^{3} d t}=\frac{t^{4}}{4}$$$ (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.

$$$\left(\frac{t^{4}}{4}\right)|_{\left(t=1\right)}=\frac{1}{4}$$$

$$$\left(\frac{t^{4}}{4}\right)|_{\left(t=0\right)}=0$$$

$$$\int_{0}^{1}\left( t^{3} \right)dt=\left(\frac{t^{4}}{4}\right)|_{\left(t=1\right)}-\left(\frac{t^{4}}{4}\right)|_{\left(t=0\right)}=\frac{1}{4}$$$

Answer: $$$\int_{0}^{1}\left( \sqrt{t^{6}} \right)dt=\frac{1}{4}=0.25$$$

Kalkulator Integral Tentu dan Tak Wajar

Hitung integral tentu dan tak wajar langkah demi langkah

Solution