Home > Calculus > Integration: the Area Problem

Let R be the region in the first quadrant enclosed by the graph of #y=2cosx#, the x-axis, and the y-axis, how do you find the area of the region R?

Answer 1

Elijah Abram

#2" sq units"#

graph{2cosx [-2.5, 7.5, -2.3, 2.7]}

the graph shows #y=2cosx#

to find the required are we need the x-coordinates where the graph crosses the x-axis in the region required

#x=0, pi/2#

#A=int_0^(pi/2)2cosxdx#

#=[2sinx]_0^(pi/2)#

#=[2sin (pi/2)]-[2sin0]#

#=2xx1=2 #

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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