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> | ||
<math> | |||
\frac{d}{dy}\left[g(y)\right] = \frac{d}{dy}\left[\int_{2}^{y}t^2\sin{(t)}dt\right] | |||
<math>= 1\cdot(y^{2}sin{(y)})-0\cdot(2^{2}sin{(2)})</math><br> | <math>= 1\cdot(y^{2}sin{(y)})-0\cdot(2^{2}sin{(2)})</math><br> | ||
<math>= y^{2} sin{(y)}</math> | <math>= y^{2} sin{(y)}</math> | ||
Revision as of 19:52, 6 September 2022
![{\displaystyle {\frac {d}{dy}}\left[g(y)\right]={\frac {d}{dy}}\left[\int _{2}^{y}t^{2}\sin {(t)}dt\right]<math>=1\cdot (y^{2}sin{(y)})-0\cdot (2^{2}sin{(2)})}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/0518285a3ddaf264aac2115732a4bbab35e6f5d6)
