   Chapter 8.1, Problem 81E

Chapter
Section
Textbook Problem

# Comparing Antiderivatives(a) Explain why the antiderivative y 1 = e x + C is equivalent to the antiderivative y 2 = C e x .(b) Explain why the antiderivative y 1 = sec 2 x + C 1 , is equivalent to die antiderivative y 2 = tan 2 x + C .

(a)

To determine

To Calculate: Whether the anti derivative y1=ex+C1 is equivalent to anti derivative y2=Cex.

Explanation

Given:

y1=ex+C1 and y2=Cex

Calculation:

Consider the two anti derivatives,

y1=ex+C1 and y2=Cex

Let,

y1=ex+C1(1).

y2=Cex(2)

Therefore, equation (1) is rewrite as,

y</

(b)

To determine
Whether the antiderivative y1=sec2x+C1 is equivalent to anti derivative y2=tan2x+C.

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