Graph of indefinite integral. please show steps

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

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And ya, its not A @Crazyandbeautiful
ok, I am waiting for your replying. Why is it not a? take integral, you have the result is??
If the polynomial \(f(x)\) has a degree of \(n\), then what can you say about the degree of \(\int f(x)\, dx\) ?
@ganeshie8 yesterday I was not online... integral of f(x) degree should be n+1
Right, Look at the given integral what is the degree of polynomial that you get after integrating ?
x^4-x^2 @ganeshie8 open study went for update, what did it update?
@ganeshie8 you there?
  • phi
can you integrate the expression?
  • 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
  • phi
there is only one curve that is an even function and (though we don't need the info), also has the correct zeros.
S, why option A is wrong? and option C is correct answer? @phi
  • 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.
ok... thats nice... so even function was the trick. thank you @phi
  • 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)
got it! Salute and Respect...!

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