FIRST FUNDAMENTAL THEOREM OF CALCULUS - PART 1

The Fundamental Theorem of Calculus (Part-1) is an extremely powerful theorem that establishes the relationship between differentiation and integration.

Using the First Fundamental Theorem of Integral Calculus, find the derivative of g(x) in each case.

Example 1 :

Solution :

Example 2 :

Solution :

Example 3 :

Solution :

Example 4 :

Solution :

g'(x) = (x³)'(cos x³) - (1)'(cos 1)

g'(x) = (3x²)(cos x³) - (0)(cos 1)

g'(x) = 3x²cos x³

Example 5 :

Solution :

g'(x) = (2x)'[(2x)³] - (x)'(x³)

g'(x) = (2)(8x³) - (1)(x³)

g'(x) = 16x³ - x³

g'(x) = 15x³

Example 6 :

Solution :

g'(x) = (x³)'(cos x³) - (x)'(cos x)

g'(x) = (3x²)(cos x³) - (1)(cos x)

g'(x) = 3x²cos x³ - cos x

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