MathDB

Let

a,\ b

be real numbers and

C

be the graph of the function y\equal{}e^{a\plus{}bx^2}. (1) Find the values of

a,\ b

such that

C

passes through the point

P(1,\ 1)

and the slope of the tangent line of

C

P

is \minus{}2. (2) For the values of

a,\ b

found in

(1)

, find the volume of the solid generated by the revolution of the part which lies in the right side for the

y

axis in the figure bounded by the parabola y\equal{}x^2 and the curve

C

about the

y

axis.

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