Question

Evaluate the following integrals:

i) \int x^5e^{x^3}dx

ii) \int_{{-4}}^{3}|x^2+x-6| dx

 

06 Feb 2021
Answer :
Word Count : 466
∫x5ex3dx
Substitute u=x3 ⟶ du/dx=3x2 (steps) ⟶ dx=1/3x2du:
=1/3∫ueudu
… or choose an alternative:
Substitute ex3
Now solving:
∫ueudu
Integrate by parts: ∫fg′=fg−∫f′g
f =u, g′ =eu
  ↓ steps   ↓ steps
f′ =1, g =eu:
___ _____ __________ _______ ______ __________.
_______ _________ _______ ______ _________.
___ ________ _______ __________ ___ _________ ________ __________ ________.
__________ ________ ___ _________ _________ ____ ___ ____ ___.
_________ ________ _______ _______ ____ ___ _____ _____ _____ ____.
______ __________ ________ ______ ______.
_______ _______ ___ ______ ______ __________ __________ ________ ______ _______ _____ ____.
_____ __________ _____ __________ ______ _____ ___ _____ _________ _______ ___ ___.
_________ ______ _____ _________ _____ ____ _______.
__________ ____ ________ ___ ______ ____ ____ _________ ______ ______ _______ ____.
___ ____ ___ _________ ________.
______ ______ ____ __________ ________ _______ ______ ________ _________ __________.
_________ ___ _____ __________ ___ ______ __________ ____ ______ ________.
________ ________ ____ _______ _____ ______ _____.
_____ ____ ________ _______ ___ _____ ________ _____ _____ __________.
__________ ___ _____ ________ _____ ___ ____.
___ _______ __________ ________ _____.
__________ _______ ___ __________ _______.
__________ ____ ________ ______ ____ _______ ____ ________ _________ ______.
_________ ________ ___ ____ ___ _________ ____ ___ ______ __________.
_______ _______ ________ __________ _____ ______ __________ _______ _________ _____.
__________ ___ _______ ____ _______ _______ ______ _____ _________ __________ ___ ____.
_________ __________ ________ _______ ____ ______ _______ _____ _____ ____ _______.
________ ____ _______ __________ _________ _____ _________ __________.
_______ _________ ______ __________ ________ ________ _______ ______ _____ _________ _________ ____.
_____ _____ _______ ______ _________ _________ ____ ___ ______ ________ _______ ____.
____ _________ __________ ______ _____ __________ _______ _______ ______ __________ ________ ___.
__________ ____ __________ ____ ___ _________ ____ _____ _______ __________.
_____ ______ _____ ___ __________ _____ ____ _________ _________.
_______ ____ ______ _____ ___ __________ ___ ________.
________ _____ _____ ______ _______ __________ _________ ____ ____ __________ ____.
_______ _____ ____ ____ _________ ___ ______ _______ _____ ______ ________ __________.
___ ______ ______ _____ _________ ____ ____ ______.
_______ _______ _____ __________ ____ _____.
__________ ___ ___ ______ ________ ___ ___ _________.
______ __________ _______ ________ ______ ____ ______ ______ ___ _____ ___.
_____ _________ ____ __________ ______ __________ __________ ___ ________ _____ _______ ________.
_________ ___.
Get Full Answer on WhatsApp
Related Questions

The cost of 2 pens, 3 note-books, and 4 books is Rs 260. The cost of 4 pens, 5 note-books, and 3 books is Rs 290. The cost of 3 pens, 2 note-books, and 5 books is Rs 320. Find the cost of 3 pens, 2 note-books and 4 books. You are bound to use the matrix techniques to solve the given equations.

If in a hall there are 10 randomly selected students then how many numbers of ways are there such that all of them have different birthday. Assume that all of them have their birth day in non-leap years

Distinguish characteristic features of each of the four measurement scales: (I) Nominal (II) Ordinal (III) Interval, and (IV) Ratio Scale. Name the measurement scale for each of the following variable.

i) Waiting time for a bus at a particular bus stop in a certain city.

ii) Number of pages in a book.

iii) Temperature in degree Celsius.

iv) Classification of cancer patients according to their severity of diseases. v) Monthly income of the family

vi) Saving (Income in that particular month − expenditure in the same month) of the family. Keep in mind that expenditure may be more than income in that particular month of some family(ies)

vii) Temperature of water by touch: cold, lukewarm and hot

viii) Height of students of a class

ix) State of residence of each student of PGDAST programme

x) Balance of Smart card of Delhi Metro hold of different passengers

Compare the following two ratio scale data sets using suitable graphical analysis tool: Score before training: 12, 17, 15, 23, 27, 21, 24, 19, 20, 23, 16 Score after training: 16, 22, 20, 24, 30, 20, 30, 17, 27, 31, 19 Also interpret the finding on the basis of the graph.

Find the sum – 7 + (– 12) + (– 17) + ... + (– 507)

An institution made a policy for delay of payment beyond a certain date to be paid by its customers. Penalty as per policy are as follows: Rs 50 for the first day, Rs 100 for the second day, Rs 150 for the third day, and so on. If a customer makes the payment on a delay of 31 days then how much he/she has to pay as penalty charges.

Express 5.10.15.20.25.30.35 in terms of factorial.

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers
Login Cart
IGNOU NEWS
Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★
Top