1. Find the antiderivative for each function when C equals 0. Check your answers by differentiation (c) (a) g(x) -5x-6 (b) Һ(х) %— х - 6 k(x)x6+3x2+4 (a) G(x) (b) Н(х) %3D (с) К(x) 3D

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Find the antiderivative for each function when C equals 0. Check your answers by differentiation
(c)
(a) g(x) -5x-6
(b) Һ(х) %— х - 6
k(x)x6+3x2+4
(a) G(x)
(b) Н(х) %3D
(с) К(x) 3D
Transcribed Image Text:1. Find the antiderivative for each function when C equals 0. Check your answers by differentiation (c) (a) g(x) -5x-6 (b) Һ(х) %— х - 6 k(x)x6+3x2+4 (a) G(x) (b) Н(х) %3D (с) К(x) 3D
Expert Solution
Step 1

Given:

(a) g(x)=-5x
(b) h(x)=x
(c) k(x)x+3x +4
Step 2

Calculation:

The reverse operation of finding a derivative is called the antiderivative
(i.e.) F'(x) f(x)
Step 3
a) g(x)-5x
J&(xd=-5x*ydc
G(x)=-5Jx*d
Step 4
Applying power rule :x"dx
a+1
-6+1
x
G(x)-5
+c,
-6+1
(c is the intergrating constant)
-5
G(x)-5
-5
G(x)x+
-5
= X
1
+c
G(x)=
G(x)+0, (given c= 0)
x
1
G(x)=
Step 5
Check:
The above function can be written as,
G(x)=x
Differentiate with respect to x
d
Applying power rule:(x")= ax"
dx
g(x)= -5(x-1)
8(x)= -5(x")
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