arindameducationusc one year ago Graph of indefinite integral. please show steps

1. arindameducationusc

see attachment

2. anonymous

a)

3. arindameducationusc

I don't need answers, I need process @Crazyandbeautiful

4. arindameducationusc

And ya, its not A @Crazyandbeautiful

5. anonymous

ok, I am waiting for your replying. Why is it not a? take integral, you have the result is??

6. ganeshie8

If the polynomial $$f(x)$$ has a degree of $$n$$, then what can you say about the degree of $$\int f(x)\, dx$$ ?

7. arindameducationusc

@ganeshie8 yesterday I was not online... integral of f(x) degree should be n+1

8. ganeshie8

Right, Look at the given integral what is the degree of polynomial that you get after integrating ?

9. arindameducationusc

x^4-x^2 @ganeshie8 open study went for update, what did it update?

10. arindameducationusc

@ganeshie8 you there?

11. arindameducationusc

@phi

12. phi

can you integrate the expression?

13. phi

ok, you have the integral x^4-x^2 factor it to get $x^2(x^2-1) \\ x^2(x-1)(x+1)$ you have zeros at x=-1, 0, and +1 because we have even exponents , it will have a $$\cup$$ shape (broadly speaking) of course, the constant of integration can shift the curve up/down

14. phi

there is only one curve that is an even function and (though we don't need the info), also has the correct zeros.

15. arindameducationusc

S, why option A is wrong? and option C is correct answer? @phi

16. phi

x^4-x^2 + C for large negative x, we get large positive y in other words, we have an even function f(x)= f(-x) or equivalently, a $$\cup$$ shape choice A has $$\cap$$ shape.

17. arindameducationusc

ok... thats nice... so even function was the trick. thank you @phi

18. phi

yes, but I just said to myself x^4 dominates x^4 has the same shape as x^2 i.e. $$\cup$$ i.e. for large x it must go up (not down)

19. arindameducationusc

got it! Salute and Respect...!