@?integration

See Also [[Maths - Integration]]S [[Maths - Integration by Substitution]]S [[Further Maths - Integrating and Differentiating Inverse Trig Functions]]S Flashcards $$\int u \frac{dv}{dx} dx$$ How can you rewrite this?? $$ uv - \int v \frac{du}{dx} $$ What table of $4$ variables should you create when doing integration by parts?/ $$ u, v, \frac{du}{dx}, \frac{dv}{dx} $$ $$\int x e^x dx$$ What are the variables you’d use for integration by parts?

See Also [[Maths - Integration]]S Flashcards $$\int (x+2)^5 dx$$ What subsitution could you make in terms of $u$?? $$ u = x + 2 $$ If $u = x + 2$, what is $\frac{du}{dx}$?? $$ \frac{du}{dx} = 1 $$ If $u = x + 2$ and $\frac{du}{dx} = 1$, what is $dx$?? $$ du $$ $$\int (x+2)^5 dx$$ If $u = x+2$ and $du = dx$, how could you rewrite the integral?

In summary, what is volumes of revolutions?? Finding volumes by integrating. Rotating the line $y = x$ around the $x$ axis creates what shape?? A cone. If you have a function $f(x)$ and an interval $[a,b]$, how can you find the volume of revolution around the $x$-axis?? $$ \int^b_a \pi f(x)^2 dx $$ If normal integration is an infinite summation of rectangles, then volumes of revolutions is an infinite summation of?? Cylinders. If you have a cylinder with radius $y$ and width $dx$, then what is the formula for the volume of that cylinder?