Standard definite integrals

standard integrals help problem 1:
Standard definite integrals

Find the value of definite integral (5- x²) with the limits 0 to 3

Solution:

Given definite integral function is, (5 - x²) dx.

Separate the given function then we get,

(5 - x²) dx =5 dx -x² dx.

=5 dx - x² dx.

= -

We know the definite integral f(x) dx = F(b) - F(a).So, Substitute upper and lower limits.

= [5(3)] - [5(0)] - [ 3³ - 0³]

= 15 - 0 - [ 27 - 0]

= 15 - 9

= 6

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