1.If \[I=\int_{1}^{2} \frac{dx}{\left(x+1\right)\sqrt{x^{2}-1}}\]
then I is equal to
a) 1
b) 2
c) \[1/\sqrt{2}\]
d) \[1/\sqrt{3}\]
Explanation:
2. \[\lim_{x \rightarrow 0} \frac{\int_{0}^{x}\sin t^{2}dt}{\sin x^{2}}\]
is
a) 1
b) 0
c) 2
d) 3/2
Explanation:
3. The value of \[\int_{-2}^{2}\mid 1-x\mid dx\]
is
a) 2
b) 0
c) 4
d) 5
Explanation:
4.If \[f\left(x\right)=\int_{0}^{x}\cos^{4}t dt\]
then \[f\left(x+\pi\right)\] equals
a) \[\frac{f\left(x\right)}{f\left(\pi\right)}\]
b) \[{f\left(x\right)}{f\left(\pi\right)}\]
c) \[{f\left(x\right)}+{f\left(\pi\right)}\]
d) \[{f\left(x\right)}-{f\left(\pi\right)}\]
Explanation:
5. Suppose that the graph of y = f (x) contains the
point (0, 4) and (2, 7). If f' is continuous then
\[\int_{0}^{2}f'\left(x\right) dx\] is equal to
a) 2
b) -2
c) 3
d) none of these
Explanation:
6. If a continuous function f satisfies \[\int_{0}^{f\left(x\right)}t^{2} dt =x^{2}\left(1+x\right)\]
for all x ≥ 0 then f (2) is equal to
a) 12
b) \[\sqrt[3]{36}\]
c) 3
d) \[\sqrt[3]{42}\]
Explanation:
7. If a continuous function f satisfies \[\int_{0}^{x^{2}}f\left(t\right) dt =x^{2}\left(1+x\right)\]
then f (4) is equal to
a) 7
b) 4
c) 5
d) 6
Explanation:
8. If \[m\neq n,m,n\epsilon N\] , then the value of \[\int_{0}^{2\pi}\cos mx \cos nx dx\]
is
a) 0
b) \[2\pi\]
c) \[\pi\]
d) dependent on m and n
Explanation:
9. The value of\[\int_{0}^{\sin^{2} x}\sin^{-1}\sqrt{t} dt+\int_{0}^{\cos^{2} x}\cos^{-1}\sqrt{t}dt\]
is
a) 0
b) \[\pi/4\]
c) \[\pi/2\]
d) \[\pi/3\]
Explanation:
10. The value of\[\int_{1/e^{2}}^{e} \mid \log x\mid dx\]
is
a) \[2\left(1-1/e^{2}\right)\]
b) \[2-3/e^{2}\]
c) \[1-2/e^{2}\]
d) \[3-2/e^{2}\]
Explanation:
