SOLUTIONS TO 1997 COLLEGE ENTRANCE EXAM - mostly Calculus, Differentiation, Integration, Areas, Volumes.

SOLUTIONS TO 1997 COLLEGE ENTRANCE EXAM - mostly Calculus, Differentiation, Integration, Areas, Volumes.

Here are the questions. Then follow my solutions :-)

SOLUTIONS ===================

Integration using substitution. (5) $\displaystyle\int_{-1}^1 {e^{\arctan x} \over 1+x^2} dx$ (12) $\displaystyle\int\sin x \cos(\cos x) dx$ (15) $\displaystyle\int_0^{1/2} {x\over \sqrt{1-x^2}} dx$ (18) $\displaystyle\int {e^{2x}\over 1+e^{4x}} dx$ (19) $\displaystyle\int e^{x+e^x} dx$ (26) $\displaystyle\int {3x^2-2\over x^3-2x-8} dx$ (27) $\displaystyle\int \cot x \ln (\sin x) dx$ (43) $\displaystyle\int e^x \sqrt{1+e^x} dx$ (34) $\displaystyle\int_{\pi/4}^{\pi/2} {1+4\cot x\over 4-\cot x} dx$

QUESTIONS: Integration using substitutions.

(5)    $\displaystyle\int_{-1}^1 {e^{\arctan x} \over 1+x^2} dx$
(12)  $\displaystyle\int\sin x \cos(\cos x)  dx$
(15)  $\displaystyle\int_0^{1/2} {x\over \sqrt{1-x^2}} dx$
(18)  $\displaystyle\int {e^{2x}\over 1+e^{4x}} dx$
(19)  $\displaystyle\int e^{x+e^x} dx$
(26)  $\displaystyle\int {3x^2-2\over x^3-2x-8} dx$
(27)  $\displaystyle\int \cot x \ln (\sin x) dx$
(43)  $\displaystyle\int e^x \sqrt{1+e^x} dx$
(34)  $\displaystyle\int_{\pi/4}^{\pi/2} {1+4\cot x\over 4-\cot x} dx$

SOLUTIONS