direct method and step down method

Step 2: Determine L and M Step 4: Integral = Lx + M log (a cos x + bsi..

Step 3: Resulting integral is evaluated by method of completing squares..

= 29.75 Calculate the mean of the question in example 4 by Short-Cut Method...

Methods of completing a square and to derive the formula for the solution of the quadratic equation. ..

which can be integrated by method of completing square..

Impure titanium is heated to 250 o C with iodine. When titanium reacts to form volatile titanium tetraiodide Impurities present in titanium do not react with iodine. Therefore, the vapors titanium tetraiodide formed is ultra pure. Vapors of titanium tetraiodide are passed through a bulb cont..

Put e x f(x) = t Differentiating w.r.t. x, {e x f(x) +e x f ' (x)} dx = dt e x {f(x) + f ' (x)} dx = dt = t + c = e x f(x)+c Evaluate the integral..

P(n,r) is the number of permutations of n dissimilar things taken r at a time. These permutations can be divided into two groups. (i) Those not containing a particular thing l . (ii) Those containing a particular thing l . Taking out l from the given things, we have (n-1) things which can be..

Similarly, (ii) and (iii) can be prov..