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Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start with finding the area between a function and the x-axis like this: What is the area? Slices.
The formulas include basic integration formulas, integration of trigonometric ratios, inverse trigonometric functions, the product of functions, and some advanced set of integration formulas. Basically, integration is a way of uniting the part to find a whole.
We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.
First, let’s look at some examples of our known methods. Basic integration formulas. 1. k dx = kx + C. xn+1. 2. xndx = + C. + 1. 3. dx = ln |x| + C. x. 4. ex dx = ex + C. 5. axdx ax. = + C ln(a) 6. sin(x) dx = − cos(x) + C. 7. cos(x) dx = sin(x) + C. 8. sec2(x) dx = tan(x) + C. 9. csc2(x) dx = − cot(x) + C. 10. sec(x) tan(x) dx = sec(x) + C.
Learn integral calculus—indefinite integrals, Riemann sums, definite integrals, application problems, and more.
BASIC INTEGRATION EXAMPLES AND SOLUTIONS. Example 1 : Integrate the following with respect to x. ∫ x 11 dx. Solution : ∫ x11 dx = x (11 + 1)/ (11 + 1) + c. = (x12/12) + c. Example 2 : Integrate the following with respect to x.
Integral Calculus. In these lessons, we introduce a notation for antiderivatives called the Indefinite Integral. We also give a list of integration formulas that would be useful to know. Share this page to Google Classroom. Related Pages. Calculus: Integration. Calculus: Derivatives. Calculus Lessons. Indefinite Integrals.
