The Fundamental Theorem of Calculus - Page 8

Questions
  • How to solve this integral ?
  • Integral 2x^3dx/(x^2 +1)^2 =ln(x^2 +1)+1/x^2 +1 +C? Thanksyou
  • What is the antiderivative of (t^2)/(t^2 + 1) dt from 1 to sq. rt. x?
  • How would you prove the Fundamental theorem of calculus?
  • Given that #int_1^3f(x)dx=3# and #int_3^6f(x)dx=5#, find: #int_1^3[f(x)+x]dx# ?
  • Find the intervals in #R# over which #∫(t+1)^3 e^t dt# from #-1# to #x# is decreasing?
  • What is the integration of #(xdx)/sqrt(1-x)#??
  • Consider the differential equation f'(x)=3x^2 -3x+5? What is the general solution for the differential equation?
  • D/dx[∫sin(t²)dt from x² to 0]=-sin(x²).This statement is true or false?Please give reasons for your answers.
  • How to derive this equation? Find a.
  • Solving this linear D.E. using an integrating factor?
  • What is #int_(1)^(oo) 1/x-1/(x-1) dx #?
  • How can you differentiate y=IN(x^2+3)?
  • #intint_D cosxy dxdy#, where #D: {[x>=0],[y>=0],[x>=y]}#?
  • If F(x)=the integration from 0 to x of square root of (t^3 + 1)dt then what is F'(2)?