MHB Definite Integral: Practice Problem Help

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A definite integral requires limits of integration, which is confirmed in the discussion. The user seeks help with a practice problem from an online worksheet provided by their professor. Participants clarify that they cannot confirm answers for graded assignments unless permitted by the instructor. The user reassures that the quiz is ungraded, but they are uncertain about one specific question. Overall, the focus remains on understanding the concept of definite integrals and the limitations of providing direct answers.
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My professor sent out an online work sheet with tons of practice problems, and I'm having trouble with this one, is my answer right? (see link) I chose this because a definite integral has to have limits, correct?

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Re: Calculus Definite Integral help?

Hi there pleashelpme, (Wave)

Yep, you are correct. A definite integral must have limits of integration, or bounds. By the way, this is just a practice assignment right? ;) We as a rule can't directly give or confirm answers for graded assignments unless the professor is ok with it.
 
Re: Calculus Definite Integral help?

Jameson said:
Hi there pleashelpme, (Wave)

Yep, you are correct. A definite integral must have limits of integration, or bounds. By the way, this is just a practice assignment right? ;) We as a rule can't directly give or confirm answers for graded assignments unless the professor is ok with it.

Thanks! No worries, it's only a practice quiz that doesn't count for a grade, but it doesn't give the answers afterwards and most of the questions I was sure about...but not this one.
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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