Question

Graph of indefinite integral. please show steps

Answer 1

see attachment

Answer 2

a)

Answer 3

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

Answer 4

And ya, its not A @Crazyandbeautiful

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

@ganeshie8 you there?

Answer 11

@phi

Answer 12

can you integrate the expression?

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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.

Answer 17

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

Answer 18

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)

Answer 19

got it! Salute and Respect...!