1
GATE ME 2005
+1
-0.3
$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx}$$ is equal to
A
$$2\int\limits_0^a {Si{n^6}x\,dx}$$
B
$$2\int\limits_0^a {Si{n^7}x\,dx}$$
C
$$2\int\limits_0^a {\left( {{{\sin }^6}x + {{\sin }^7}x} \right)dx}$$
D
zero
2
GATE ME 2005
+1
-0.3
Changing the order of integration in the double integral
$${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{\scriptstyle x} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}}^2 {f\left( {x,\,y} \right)dy\,dx} }$$ leads to $$\,{\rm I} = \int\limits_r^s {\int\limits_p^q {f\left( {x,\,y} \right)dy\,dx} } .$$ What is $$q$$?
A
$$4y$$
B
$${16{y^2}}$$
C
$$x$$
D
$$8$$
3
GATE ME 2004
+1
-0.3
If $$\,\,\,x = a\left( {\theta + Sin\theta } \right)$$ and $$y = a\left( {1 - Cos\theta } \right)$$ then $$\,\,{{dy} \over {dx}} = \,\_\_\_\_\_.$$
A
$$Sin{\theta \over 2}$$
B
$$Cos{\theta \over 2}$$
C
$$Tan{\theta \over 2}$$
D
$$Cot{\theta \over 2}$$
4
GATE ME 1999
+1
-0.3
Value of the function $$\mathop {Lim}\limits_{x \to a} \,{\left( {x - a} \right)^{x - a}}$$ is _______.
A
$$1$$
B
$$0$$
C
$$\infty$$
D
$$a$$
GATE ME Subjects
EXAM MAP
Medical
NEET