Choose the best answer for each question, then mark the corresponding letter in the blank
3^(')\times 5=15^(')
(1) Suppose that
\int_0^1 f(x)dx=4 and
\int_1^2 f(x)dx=-2, then
\int_0^2 f(x)dx=
◻
(A) 2
(B) 6
(C) -2
(D) -6
(2) If
f(x)=sin^(-1)lnx, then the derivative of
f(x) is
◻
(A)
(cos^(-1)lnx)/(x)
(B)
(1)/(x\sqrt(1+ln^(2)x))
(C)
(1)/(x\sqrt(1-ln^(2)x))
(D)
(1)/(x(1+ln^(2)x))
(3) Which one is the antiderivative of
sec^(2)x in the following option
◻
(A)
tanx
(B)
secxtanx
(C)
tan^(2)x
(D)
cosx
(4) Suppose the solid is obtained by rotating the region bounded by the curves
y=x and
y=x^(2) about the
y-axis, then the volume of this solid is
◻
(A)
\pi \int_0^1 (x^(2)-x^(4))dx
(B)
\pi \int_0^1 (x^(4)-x^(2))dx
(C)
\pi \int_0^1 (y^(2)-y)dy
(D)
\pi \int_0^1 (y-y^(2))dy
(5) When evaluate the integral
\int x^(2)\sqrt(x-1)dx, the substitution is
◻ (A)
x=sin\theta
(B)
x=sec\theta
(C)
x=tan\theta
(D)
u=\sqrt(x-1)
