5.3 The Fundamental Theorem of Calculus/9: Difference between revisions
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<math>g(y)= \int_{2}^{y}t^2\sin{(t)}dt</math><br> | <math>g(y)= \int_{2}^{y}t^2\sin{(t)}dt</math><br><br> | ||
= 1\cdot(y^{2}sin{ | |||
= y^{2} sin{(y)} | <math> | ||
\frac{d}{dy}\left[g(y)\right] = \frac{d}{dy}\left[\int_{2}^{y}t^2\sin{(t)}dt\right] | |||
= 1\cdot((y)^{2}\sin{y})-0\cdot((0)^{2}\sin{(2)}) | |||
= y^{2}\sin{(y)} | |||
</math> | |||
<math> | |||
\text{Therefore, } g'(y) = y^{2}\sin{(y)} | |||
</math> | </math> | ||
Latest revision as of 20:14, 6 September 2022
![{\displaystyle {\frac {d}{dy}}\left[g(y)\right]={\frac {d}{dy}}\left[\int _{2}^{y}t^{2}\sin {(t)}dt\right]=1\cdot ((y)^{2}\sin {y})-0\cdot ((0)^{2}\sin {(2)})=y^{2}\sin {(y)}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/95fa152b3d3ba4f0fae375aa07a9effd08e165d2)
