Methods of Solving Integral Calculus Problems

As mentioned in the previous posts that there are two types of integral problems that a student would encounter during the class of Integral Calculus. This post would provide help and tutorial on how to solve indefinite integrals.

For finding solution of indefinite integrals, basically you have to use any of the three approaches that are applying basic formulas, simplifying the algebraic expressions given in the problem and using substitution method.

Previous post of our blog of homeworkhelpexperts. com gives you the details list of basic formula that a student can apply for finding solution of Integral Calculus problems. For example if the given function is f(x) = x5 than integration of this would be using formula of xn be (x6/6) +C.

Second method of solving indefinite integrals is simplifying algebraic expressions. In this approach, we should observe the algebraic expression given. If it does not fit in the basic formula, we should try to see if we can simplify the given the algebraic expression.

For examples if the given algebraic expression is (2x+1)2 than it can be observed that it cannot be solved by basic formulas. Our next step shall be such that we should expand the given equation. After expanding the given equation, it would become 4x2 + 4x + 1. Now expression (4x2 + 4x + 1) can be solved using basic formulas if we separate this expression in three basic integrals. Similar to this, another example is (x2 +x)/x and this expression can be simplified as (x+1).

Third method of solving integrals is by substitution and in this method we use differentiation by identifying which is the differentiable function. For example if v = h(x) is differentiable function and g is a continuous function in the range of the function h(x), then it can be represented as below

By taking an example , this integral can be solved using substitution method.

Putting t = x6 + 9, that implies dt = 5x5 dx =5 x5 dx. So, our original expression reduces tothat can be easily solved using basic formulas.

So as described above, one needs to follow any of these three methods to solve an integral problem. Most important for handling your homework and assignments regarding integral problems is that you should focus on what kind of expression is given to you in the problem. Other important thing is that you should know and memorise the basic formulas of integral calculus. These basic skills you can learn maximum by practicing as much as possible. So to master these skills, it is very important that you solve as many problems as possible from your text book.

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