The most common integration formulas include: Constant rule: ∫c dx = cx + C, where c is a constant. Power rule: ∫x^n dx = (x^ (n+1))/ (n+1) + C, where n ≠ -1.

Practice set 1: Integration by parts of indefinite integrals. Let's find, for example, the indefinite integral \displaystyle\int x\cos x\,dx ∫ xcosxdx. To do that, we let u = x u = x and dv=\cos (x) \,dx dv = cos(x)dx: u=x u = x means that du = dx du = dx. dv=\cos (x)\,dx dv = cos(x)dx means that v = \sin (x) v = sin(x). Now we integrate by.

Physics Formulas Associated Calculus Problems Mass: Mass = Density * Volume (for 3‐D objects) Mass = Density * Area (for 2‐D objects) Mass = Density * Length (for 1‐D objects) Mass of a one‐dimensional object with variable linear density: () bb aadistance

The integration of tanx is – log |cos x| + C or log |sec x| + C. i.e. ∫ (tanx) dx = – log |cos x| + C or, ∫ (tanx) dx = log |sec x| + C.

The Fundamental Theorem of Calculus, Part 1 shows the relationship between the derivative and the integral. The Fundamental Theorem of Calculus, Part 2 is a formula for evaluating a definite integral in terms of an antiderivative of its integrand. The total area under a curve can be found using this formula.

The integration by parts formula is used to find the integral of a product. In the product rule of differentiation where we differentiate a product uv, u (x), and v (x) can be chosen in any order.