Question

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$

Evaluate $\textstyle\int{\frac{\cos{\sqrt{x}}}{\sqrt{x}}}\,d x\ .$

If f(x) = 27x³ and g(x) = $x^{1/3}$, then find gof(x).

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.

Write the degree of the differential equation : $x\left(\frac{d^{2}y}{d x^{2}}\right)^{3}+y\left(\frac{d y}{d x}\right)^{4}+x^{3}=0$

Find ‘λ’ when the projection of $\stackrel{\rightarrow}{a}\$ = $λ\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ on $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ is 4 units.