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Friday, November 18, 2016

PARTS OF SPEECH


PARTS OF SPEECH

NOUNS
A noun is a word used as the name of a person, place or thing.
Examples: King, Mohan, Sarita, Mumbai, Table

PRONOUNS
A pronoun is a word used instead of a noun.
Examples: He, She, It, They

ARTICLES
The words ‘a’, ‘an’ and ‘the’ are called articles. They are used before nouns.

VERBS
A verb is a word that describes an action or occurrence or indicates a state of being.
Examples: He talks to Sameer, She sings
a song

ADJECTIVES
An adjective is a word used to describe a noun.
Examples : Beautiful house, Tall man
ADVERBS
An adverb is a word which modifies the meaning of a verb, adjective or another adverb.
Examples: He runs fast, They fought bravely.

PREPOSITIONS
A preposition is a word which shows the relation between the noun or pronoun and other words in the sentence.
Examples: The boy is in the room, The book is on the table.


CONJUNCTIONS
A conjunction is a word which joins to sentences to complete their meaning.
Examples : They reached the station but it was too late.
He put on his shoes because he was going for a run.

INTERJECTIONS
An interjection is a word which expresses sudden feeling or emotion.
Examples : Hello!, Alas!, Hurray!, Oh!


Sunday, November 13, 2016

How to Integrate Sin^2 X


How to Integrate Sin^2 X

The solution to the integral of sin^2(x) requires you to recall principles of both trigonometry and calculus. Don't conclude that since the integral of sin(x) equals -cos(x), the integral of sin^2(x) should equal -cos^2(x); in fact, the answer does not contain a cosine at all. You cannot directly integrate sin^2(x). Use trigonometric identities and calculus substitution rules to solve the problem.
Use the half angle formula, sin^2(x) = 1/2*(1 - cos(2x)) and substitute into the integral so it becomes 1/2 times the integral of (1 - cos(2x)) dx.
Set u = 2x and du = 2dx to perform u substitution on the integral. Since dx = du/2, the result is 1/4 times the integral of (1 - cos(u)) du.
Integrate the equation. Since the integral of 1du is u, and the integral of cos(u) du is sin(u), the result is 1/4*(u - sin(u)) + c.
Substitute u back into the equation to get 1/4*(2x - sin(2x)) + c. Simplify to get x/2 - (sin(x))/4 + c.

Integral of tan^4x

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integrate tan^4 x dx

How to integrate sin(2x) - First time

How to integrate sin(2x) - First time

Tuesday, November 1, 2016

FINITE AND NON-FINITE VERBS


FINITE AND NON-FINITE VERBS
Identify the finite and non-finite verbs in the following sentences.
1. My little brother wants to be an actor.
2. She worked hard to pass the test.
3. I couldn’t solve the problem.
4. To err is human.
5. Your duty is to cross the river without getting noticed.
6. The doctor is attending to the injured people.
7. She opened the door.
8. The students were asked to submit their assignments by Friday.
9. The teacher encouraged the students to work hard.
10. The dog wagged its tail to show its happiness.
Answers
1. My little brother wants to be an actor. (wants – finite; to be – non-finite)
2. She worked hard to pass the test. (worked – finite; to pass – non-finite)
3. I couldn’t solve the problem. (couldn’t solve – finite)
4. To err is human. (to err – non-finite; is – finite)
5. Your duty is to cross the river without getting noticed. (is – finite; to cross – non-finite; getting – non-finite)
6. The doctor is attending to the injured people. (is attending – finite)
7. She opened the door. (opened – finite)
8. The students were asked to submit their assignments by Friday. (were asked – finite; to submit – non-finite)
9. The teacher encouraged the students to work hard. (encouraged – finite; to work – non-finite)
10. The dog wagged its tail to show its happiness. (wagged – finite; to show – non-finite)