{"id":492,"date":"2017-10-05T11:25:13","date_gmt":"2017-10-05T05:55:13","guid":{"rendered":"http:\/\/ibelitetutor.com\/blog\/?p=492"},"modified":"2024-05-21T15:49:28","modified_gmt":"2024-05-21T10:19:28","slug":"indefinite-integration-in-ib-mathematics","status":"publish","type":"post","link":"http:\/\/ibelitetutor.com\/blog\/indefinite-integration-in-ib-mathematics\/","title":{"rendered":"Indefinite Integration-Topics in IB Mathematics"},"content":{"rendered":"

Indefinite Integration<\/span><\/h2>\n

After a long series on differentiation and ‘Application of derivatives’, Online IB Tutors<\/strong> will now discuss Indefinite Integration. It consists of two different words indefinite and integration by\u00a0IB Maths Tutors .<\/strong>
\nFirst of all, we shall learn about Integration.<\/p>\n

\u00a0<\/strong>Integration is the reverse process of\u00a0differentiation so we can also call it as antiderivative. There is one more name for it, that is Primitive.
\nIf f & g are functions of x such that g'(x) = f(x) then the function g is called a Primitive Or Antiderivative Or Integral of \u00a0f(x) w.r.t. x and is written symbolically as:-<\/p>\n

\"\\int <\/p>\n

If \u00a0 \u00a0\"\\frac{d}{{dx}}\\left\\{<\/p>\n

then \u00a0\"\\int\u00a0 \u00a0 \u00a0here c is just an arbitrary constant. Value of c is not definite that’s why we call it Indefinite Integration.<\/strong><\/p>\n

Techniques \u00a0Of \u00a0Integration-:<\/strong> <\/span><\/h3>\n

There are a few important techniques used to solve problems based on an integration<\/p>\n

(i)<\/strong> Substitution or \u00a0Change of Independent Variable- <\/strong>If the derivative of a function is given in the question, then we should use the method of substitution to integrate that question.<\/p>\n

Example-1<\/strong> Find integration of this problem \u00a0\"\\int\u00a0<\/span><\/p>\n

Ans- Here derivative of \u00a0<\/span>\"{x^2}\"\u00a0is 2x that is given in the question so we can substitute\u00a0\u00a0<\/span>\"{x^2}\"\u00a0by some other variable. let \u00a0<\/span>\"{x^2}\"=t<\/p>\n

If we differentiate both sides
\n2x.dx=dt<\/p>\n

so \u00a0\"\\int\u00a0= \u00a0\"\\int\u00a0+c<\/p>\n

(ii) Integration by part-<\/strong>\u00a0If we are given the product of two functions such that we are not able to use the method of substitution to integrate it, then we use Integration by parts. Suppose u and v are two functions then-<\/p>\n

\"<img<\/a><\/p>\n

Note-:<\/span> While using integration by parts, choose u \u00a0& \u00a0v \u00a0such that we can easily apply above formula and reduce the given function from a product of two functions into a function that can be easily integrated. For this, we choose u in the order of ILATE.<\/span> Here
\nI\u00a0\"\u00a0inverse function<\/p>\n

\u00a0L\"\u00a0Logarithmic Functions<\/p>\n

A\"\u00a0 Algebraic Functions<\/p>\n

T\u00a0\"\u00a0Trigonometric functions<\/p>\n

E\u00a0\"\u00a0Exponential function<\/p>\n

Some people use the above formula in a different way<\/p>\n

they choose F(x) in this order: LIPET<\/span><\/p>\n

logs, Inverse, Polynomial, exponential, trigonometric<\/p>\n

(iii) Integration by Partial Fractions- <\/strong>Partial fraction is a long and different topic. We use it in integration to simplify some complex fraction. I have attached a whole module on this topic at the end of the post<\/p>\n

(iv) When the Power of Numerator is More Than the Power of Denominator- <\/strong>In this case, we first divide the numerator by denominator to make it a pure fraction, then we can use the partial fraction to simplify and integrate it.<\/p>\n

Integrals Of Some Special Type-<\/strong><\/span><\/h4>\n

Here we have some special types of functions and tricks to integrate them.<\/span><\/p>\n

(i) \u00a0\"{\\int\u00a0 or \u00a0\u00a0\"\\int\u00a0in these cases, we let f(x)=t<\/p>\n

(ii) \u00a0\u00a0\"\\int, \"\\int\u00a0\u00a0\"\\int\u00a0in all these cases we convert<\/p>\n

(\"{a{x^2}) into a perfect square\u00a0<\/p>\n

(iii) \u00a0\u00a0\"\\int\u00a0 \u00a0,\u00a0\"\\int\u00a0in these cases we\u00a0Express:-<\/p>\n

px + q = A (differential co-efficient of denominator) + B<\/p>\n

(iv) \u00a0\u00a0\"\\int<\/p>\n

(v) \u00a0\"\\int<\/p>\n

<\/p>\n

(vi) \u00a0\u00a0\"\\int<\/p>\n

(vii) \u00a0 \u00a0\"\\int\u00a0 \u00a0 \u00a0<\/span>\"n\u00a0in this case, we <\/span>take \u00a0\u00a0\"{x^n}\"\u00a0 \u00a0common and put \u00a0<\/span>\"1= t<\/span><\/p>\n

(ix) \u00a0\u00a0\"\\int\u00a0 \u00a0\u00a0\"n\u00a0in this case, we take \u00a0\u00a0\"{x^n}\"\u00a0 \u00a0common and put \u00a0\"1= t \u00a0 If we<\/p>\n

If we take care of all these rules properly, then we can solve all the problems of definite integration.<\/p>\n

Here I am attaching a full module on Integration by Partial fraction
\nA pdf containing almost all formulas of indefinite integration
\nA pdf of a few questions based on the integration<\/p>\n

\u200b<\/p>\n

\u200b\u200bIn the next post, I shall discuss Definite integration<\/h3>\n

Hire the best IB Maths Tutors<\/strong><\/a> and IB Tutors in Delhi<\/strong> and get the best grades<\/p>\n

\"ib<\/p>\n\n

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    <\/ul><\/div>\n
    \n
    \n<\/fieldset>\n

    \n<\/p>

    <\/div>\n<\/form>\n<\/div>\n\n

    <\/p>\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    Indefinite Integration After a long series on differentiation and ‘Application of derivatives’, Online IB Tutors will now discuss Indefinite Integration. It consists of two different […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-492","post","type-post","status-publish","format-standard","hentry","category-ib-mathematics-tutors"],"_links":{"self":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/posts\/492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/comments?post=492"}],"version-history":[{"count":0,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/posts\/492\/revisions"}],"wp:attachment":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/media?parent=492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/categories?post=492"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/tags?post=492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}