Given a derivative, f0(x), the process of finding the function f(x) is called antidifferentiation or integration. The most general function f(x) is called ...

Find the indefinite integral of f(x)=(x2 + 1)2x. Solution. Let u = x2 + 1, du = 2xdx so that. ∫. (x2 + 1)2xdx = ∫ 1. 2 u2du = 1. 2. 1. 3 u3 + C = 1.

#XE (a, b), then f(x)=6(x) + k constant k. antiderivative (aka. indefinite integral) family of solutions on. (a, b). Notation: If. F(x)= f(x), then {f(x) dx.

Find the indefinite integral of the given function: a) f x x2. 3x x 2. Answer. f x dx x3. 3. 3. 2 x2 x 1 C b) g x sinx. 1 cos2 x. Answer. g x dx cosx tanx C ...

Examples. 1. The monthly marginal cost for a product is MC = x+ 30. If fixed costs are $50, find the total cost function for the month.

Find the indefinite integrals of the following functions. 1. arccosx. 1 x2 dx. 2. lnx 1 2 x dx. 3. cos3 xsin2 xdx. 4. dx x2 x 1. 5. x x 1 dx. 6. dx x.

Sometimes we can conclude that the improper integral converges, even though we cannot calculate the actual limit. This is because of the following fact: Theorem ...

... (x), but I = x a f (t)dt. So, to calculate a definite integral b a f (x)dx, follow these steps: 1. Find an indefinite integral F for f;. 2. Evaluate F (b)- F(a).

g(x) = sin x + 1 / cos2 x . ∫ g(x)dx = -cos x + tan x + C since 1 / cos2 x = sec2 x . \leqno{ Solution}. ∋ 8. Find the indefinite integral of h(x)= tan x sec2 ...

The method of quadrature refers to the technique of integrating both sides of an equation, hoping thereby to extract a solution formula.