Question
The area of the region bounded by the lines x x = 0, 2, = and y = 0 and the curve \(y=e^{\frac{x}{2}}\) is
(A)\(\frac{e-1}{2} \) (B) e −1 (C) 2 (e −1 ) (D) 2 e −1 (E) 2e
▶️Answer/Explanation
Ans:C
\(Area =\int_{0}^{2}e^{\frac{x}{2}} dx=2e^{\frac{x}{2}}\)
Question
What is the area of the region completely bounded by the curve \(y=-x^{2}+x+6\) and the line y = 4 ?
(A) \(\frac{3}{2}\)
(B) \(\frac{7}{3}\)
(C) \(\frac{9}{2}\)
(D) \(\frac{31}{6}\)
(E) \(\frac{33}{2}\)
▶️Answer/Explanation
Ans:C
Question
If\( y = 2x – 8\) , what is the minimum value of the product xy ?
(A) –16 (B) –8 (C) –4 (D) 0 (E) 2
▶️Answer/Explanation
Ans:B
\(p(x)=2x^2-8x;P'(x)=4x-8;p\)’; changes from negative to positive at x= 2.p (2)= 8