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SOLUTION :
1.
b
Area = ∫ [f(x) - g(x)] dx
a
where,
a = 0 , b = 2π
f(x) = cos(x) + 5 and g(x) = cos(x) + 3
=> f(x) - g(x) = 2
So,
Area
2π
= ∫ 2 dx
0
2π
= [ 2x ]
0
= 4π (ANSWER)
2.
b
Area = ∫ [f(x) - g(x)] dx
a
where,
a = 4 , b = 7
f(x) = √(x - 4) + 3 and g(x) = - x + 7
=> f(x) - g(x) = √x - 4) + 3 + x - 7 = (x - 4)^(1/2) + x - 4
So,
Area
7
= ∫ ( (x - 4)^(1/2) + x - 4 ) dx
4
7
= [ 2/3 (x - 4)^(3/2) + x^2 /2 - 4x ]
4
= [ (2/3 (7 - 4)^(3/2) + 7^2 /2 - 4*7) - (2/3 (4 - 4)^3/2 + 4^2/2 - 4*4) ]
= 2/3 * 3 √3 - 7/2 + 8
= 2√3 + 9/2 = 7.96 (ANSWER)
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