integral of sinx 3

Step 1: By method of completing squares Step 2: Use standard and integrals and evaluate Step 1: put px + q = L (2ax + b) + M and determine L and M. Step 3: Second integral on the right hand side can be evaluated by method of completing squar..

? If the derivative of a function is given, then the function itself is called anti-derivative or integral. We illustrate it with the help of an example. Consider the function f(x) = x 4 then its derivative is given by f ' (x) = 4x 3 . The question arises: given f ' (x) = 4x ..

Consider the following example: Let f(x) = cos 3x, let us find a function F(x) such that We know that Here In other words we say the integral cos 3x is Suppose then also we ha..

When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference. (1) (2) (3) (4) (5) (7) (..

], which is shown in the figure. Being a rectangular region, the area of f(x) = 2 bounded by X- axis, x = 1 and x = 2 is given by base X height, the height being equal to Base = (2 - 1) = 1 units, height = 2 units This region is triangular above the axis bounded by x = 0 and x = 1. The area of this..

> The circum-oesophageal nerve ring is ring-like structure around the oesophagus. It consists of supra-oesophageal ganglion or brain, circum-oesphageal connective and the sub-oesophageal ganglion. Ventral Nerve cord - has 3 thoracic ganglia and six are the abdominal ganglia. The periphera..

Working rules for expanding (a + b) n n N: Step 1: The value of index, n implies that there will be n+1 terms in the expansion of (a + b) n . Step 2: Write the first term: n C 0 a n b 0 . Step 3: For the second term, take coefficient as n C 1 , decrea..

Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Writ..

By the method of induction, prove that 10 n + 3 · 4 n + 2 + 5 is divisible by 9 for all positive integral values of n ...

Evaluate the definite integral ∫ -1 0 ( x 3 + 1) dx => - 3 or 3 4 or 1 or 0 or - 1..