ZHENG YONG TAN's answer to help's Secondary 4 A Maths Singapore question.
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take note that I added a negative sign before and after the integration sign to the expression so the integration would be more straightforward
to do integration you have to be comfortable with your differentiation first, and then the integration will come to you much more easily.
do let me know in the comment if you still have any trouble. goodluck!
to do integration you have to be comfortable with your differentiation first, and then the integration will come to you much more easily.
do let me know in the comment if you still have any trouble. goodluck!
Date Posted:
2 years ago
where did -sinx go integrate -sinx dont you get cos x so isnt it -cosx/sinx e ^cos x
you can see that the expression that you are required to integrate is already in the form of f'(x)e^[f(x)].
- for the integration for f'(x)e^[f(x)], we simply get e^[f(x)] + C
- you can see that the differential of cosx is -sinx
- the expression is already somewhat in the form of f'(x)e^[f(x)], however you need to add a negative sign inside and outside of the integral to get the needed form
- then you can integrate to get -e^cos(x) + C
the -sinx is the f'(x) in f'(x)e^[f(x)], and so when you integrate it just becomes e^[f(x)] which is e^cos(x) +C
- for the integration for f'(x)e^[f(x)], we simply get e^[f(x)] + C
- you can see that the differential of cosx is -sinx
- the expression is already somewhat in the form of f'(x)e^[f(x)], however you need to add a negative sign inside and outside of the integral to get the needed form
- then you can integrate to get -e^cos(x) + C
the -sinx is the f'(x) in f'(x)e^[f(x)], and so when you integrate it just becomes e^[f(x)] which is e^cos(x) +C
i still dont get it if i integrate sinx e^cos x shouldnt i integrate sinx = -cosx and integrate e^cosx = 1/-sinx e^cosx so overall integrate sinx e^cos x = cosx/sinx e^cosx = tanx e^cosx
but then when i differentiate it back its wrong so im so confused
but then when i differentiate it back its wrong so im so confused
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