Let f(x) be a continuous and differentiable function such that f(x)=∫0xsin(t2−t+x)dt Then prove that f′′(x)+f(x)=cosx2+2xsinx2

Click here to view the solution.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Let {f{{({x})}}} be a continuous and differentiable function s

Question

Let $f (x)$ be a continuous and differentiable function such that $f (x) = \int_{0}^{x} sin (t^{2} - t + x) d t$ Then prove that $f^{^{''}} (x) + f (x) = cos x^{2} + 2 x sin x^{2}$

Views: 692 students

Found 6 tutors discussing this question

Sofia Discussed

Let

f (x)

be a continuous and differentiable function such that

f (x) = \int_{0}^{x} sin (t^{2} - t + x) d t

Then prove that

f^{^{''}} (x) + f (x) = cos x^{2} + 2 x sin x^{2}

7 mins ago

Discuss this question LIVE

7 mins ago

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text

Let

f (x)

be a continuous and differentiable function such that

f (x) = \int_{0}^{x} sin (t^{2} - t + x) d t

Then prove that

f^{^{''}} (x) + f (x) = cos x^{2} + 2 x sin x^{2}