Calculus chapter7 (Transcendental Functions)
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1)

2)

3)

Step-by-step explanation:

1)

This integral can be solved easily by using algebraic substitutions:

,

Then, the integral can rewritten as follows:

Where is the integration constant.

2) Let be , then we obtain the expression by the definition of the derivative for the inverse hyperbolic cosine and the chain rule:

3)

This integral can be solved by the following trigonometric substitutions:

Where is the integration constant.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."