4. Integration
Interactive practice questions
The function $f$f has an antiderivative $F$F, and $F\left(3\right)=4$F(3)=4.
a
Express $\int_3^xf\left(t\right)dt$∫x3f(t)dt in terms of $F$F and $x$x.
b
Now, calculate $\frac{d}{dx}\int_3^xf\left(t\right)dt$ddx∫x3f(t)dt.
Easy
6min
Consider the function $f\left(t\right)=-4t$f(t)=−4t.
Easy
4min
Consider the function $f\left(t\right)=12t+9$f(t)=12t+9.
Easy
3min
Calculate $\frac{d}{dx}\int_2^x\left(6t^2-8t+3\right)dt$ddx∫x2(6t2−8t+3)dt.
Easy
1min
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