Let $$ I=\int e^x/(e^{4x}+e^{2x}+1) dx$$ $$ J= \int e^{-x}/(e^{-4x}+e^{-2x}+1)dx$$. Find the value of \(J-I\). Solution: $$ I=\int e^x/(e^{4x}+e^{2x}+1) dx$$ $$J= \int e^{-x}/(e^{-4x}+e^{-2x}+1)dx$$ Let \(e^x\)=\(z\) $$...

Consider an expression F=Ax\(sin^{-1} (Bt)\) where F represents force, x represents distance and t represents time. Dimensionally the quantity AB represents (A) energy (B) surface tension (C) intensity of light (D) pressure Solution: The quantity Ax on RHS must have...

The distance travelled by an object is given by x=(at+bt2)/(c+a) where t is time and a,b,c are constants. The dimension of b and c respectively are: [L2T-3], [LT-1] [LT-2], [LT-1] [LT-1], [L2T1] [LT-1], [LT2] Solution: The dimension of x is L. Hence, the dimension of...