Wati lg
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The document discusses indefinite integrals and their relationship to derivatives. It states that the indefinite integral is the inverse of the derivative, so finding the integral of a function means finding its antiderivative. The document provides examples of using formulas to find the antiderivatives of functions like 5x^4 by recognizing it as the derivative of x^5. It also demonstrates how integrals follow properties like scalar multiplication and addition/subtraction.
Wati lg
- 1. INTEGRAL Indefinite Integral In calculus integral known are two concept,namely indefinite integral and definite integral.Concept of the indefinite integral is the inverse of derivative. Integraling a derivative function f(x)=f(x) means we seek integral or anti-derivtive,is f(x),if the function is derived produce original function f(x). If F(x) = f(x) so F(x) is an anti-derivative from f(x) Example :find the anti-derivative from =5x4
- 2. Solution Determine the function f(x) derivatives is f(x) = 5x4.we know that if F(x) = xn,so F(x) =f(x) =nxn-1.so that if nxn-1=5x4 so n-1= 4 and n = 5 so that,x5 is an anti-derivatiive of 5x4 general integral of function f written
- 3. Example : Compute the integral of the following functions 3dx Solution : we will just plug into the formula,and the integral above n= 3. 3 dx = x3+1 + C = x4 + C
- 4. Integral scalar multiplication for every real number k Example :compute the integral of the following function 3 dx Solution :we will just plug into the formula 3 dx =2 3 dx =2 ( x4 ) + C = x4 + C
- 5. Integral use Addition and Reduction Example :find the integral of the following finction 2 - 4x +5) dx Solution : we will just plug into the formula 2 4x + 5) dx = 3 2 dx 4 +5 = 3 ( x3 ) 4( x2) + 5x + C = x3 2x2 + 5x + C