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Class 12

MATHS

DEFINITE INTEGRALS

Updated On: 5-4-2021

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Transcript

Time | Transcript |
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00:00 - 00:59 | hello guys the question is a integration from lower limit is 0 an upper limit is pi by 2 and the function is root of cos theta multiply with sin cube theta detector now here we know that sin square theta + cos square theta equal to 1 so we can write sin square theta is equal to 1 minus cos square theta in our integration of 0 to pi by 2 root over cos theta and we can write sin square theta multiply sin theta deta now we can write 0 to pi by 2 root over cos theta and sin square theta we can write a diary 1 - cos square theta and sin theta deta now now we take cos theta is equal to T not differentiate on both |

01:00 - 01:59 | side you will get minus sin theta theta is equal to DP now put the value of theta is equal to 1 by sin theta minus sin theta now here we get 0 to 5 by 2 and root over cos theta is we can write root 3 and 1 - cos square theta by 1 minus A square and multiply digitised by minus sin theta sin theta x minus sin theta so sin theta sin theta cancel and we will get - of 0 to pi by 2 and root tea and 1 - 30 square DT now you know that we assume cos theta is equal to 3 not change the value of limit that is put cause jio 40 is equal to chhutti |

02:00 - 02:59 | chhutti is equal to 1 and now Cos pi by 2 Cos pi by 2 is equal to 3 is equal to zero now we change the limit according to tea so that is 120 - of root 3 and minus 3 1 by 2 + Tu that is dirty that is DDT so it is equal to minus of 120 and T power 1 by 2 minus 3 power that is 4 + 1 is 5 by 2 DP now integration of x power n is equal to x power n + 1 / and + 1 + c so it is equal to minus |

03:00 - 03:59 | 120 and integration is this is the interval and integration becomes the power 1 by 2 + 1 is 3 by 2 and 3 by 2 minus of T1 5 by 2 + 1 is 7 by 27 vi to so this is the integration of our function now put the now this is equal to minus put so it is equal to zero 0 and when you put the upper limit that we comes with zero because here is the and here is it so it becomes zero and minus of minus of t 3 by 2 minus of T 72 72 now put the limit as one so when you put the limit here as |

04:00 - 04:59 | 1 this is power 3 by 2 you will get + of 2 by 3 minus of 27 now this is equal to this is equal to taking LCM 21 you will get for 3 - 6 that is equal to 8 by 21 so our answer is 8 by 21 thank you |

A function

Some important formulas of integration

Examples of integration: (i)

Theorem:

The integral of the product of a constant and a function = the constant x integral of function

Geometrical interpretation of indefinite integral

Comparison between differentiation and integration

By substitution: Theorem: If

Examples:

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