5.3 The Fundamental Theorem of Calculus/27: Difference between revisions
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= \left(\frac{2x^2}{1+1}+\frac{x^6+1}{6+1}\right)\bigg|_{0}^{2}=\left(x^2+\frac{x^7}{7}\right)\bigg|_{0}^{2} | &= \left(\frac{2x^2}{1+1}+\frac{x^6+1}{6+1}\right)\bigg|_{0}^{2}=\left(x^2+\frac{x^7}{7}\right)\bigg|_{0}^{2} | ||
= \left((2)^2+\frac{(2)^7}{7}\right)-\left((0)^2+\frac{0^7}{7}\right) | &= \left((2)^2+\frac{(2)^7}{7}\right)-\left((0)^2+\frac{0^7}{7}\right) | ||
= 4+\frac{2^7}{7} | &= 4+\frac{2^7}{7} | ||
= \frac{156}{7} | &= \frac{156}{7} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 21:04, 6 September 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int_2^0 x(2+x^5)\,dx = \int_2^0 (2x+x^6)\,dx &= -\int_0^2 (2x+x^6)\,dx &= \left(\frac{2x^2}{1+1}+\frac{x^6+1}{6+1}\right)\bigg|_{0}^{2}=\left(x^2+\frac{x^7}{7}\right)\bigg|_{0}^{2} &= \left((2)^2+\frac{(2)^7}{7}\right)-\left((0)^2+\frac{0^7}{7}\right) &= 4+\frac{2^7}{7} &= \frac{156}{7} \end{align} }