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nevsk [136]
3 years ago
11

Which of the following integrals represents the area of the region bounded in the first quadrant by x = pi/ 4 and the functions

f(x) = sec^2(x) and g(x) = sin(x)?

Mathematics
1 answer:
Kaylis [27]3 years ago
7 0

Answer:

option B is true.

Step-by-step explanation:

We are given that two functions

f(x)=sec^2x and g(x)=sin x and a line x =\frac{\pi}{4}

We have to find the area of the region bounded in the first quadrant by x={\pi}{4} and two functions

We know that the area bounded by two functions

=Integration of region(Upper curve- lower curve)

Therefore, function of sec square x is upper curve and function of sin x is lower function

Therefore, limit of x changing from 0 to \frac{\pi}{4}

Hence, the area of the region bounded in the first quadrant and two functions is given by

=\int_{0}^{\frac{\pi}{4}} (sec^2x-sinx) dx

Therefore, option B is true.

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