Write True or False `C(x)= int MC dx +c`

Write a value of inte^(a x)sinb x\ dx

Write true or false for the following statements: Steam at 100^(@)C causes more severe burns than water at 100^(@)C _________.

If y=f(x) is a monotonic function in (a,b), then the area bounded by the ordinates at x=a, x=b, y=f(x) and y=f(c)("where "c in (a,b))" is minimum when "c=(a+b)/(2) . "Proof : " A=int_(a)^(c)(f(c)-f(x))dx+int_(c)^(b)(f(c))dx =f(c)(c-a)-int_(a)^(c) (f(x))dx+int_(a)^(b)(f(x))dx-f(c)(b-c) rArr" "A=[2c-(a+b)]f(c)+int_(c)^(b)(f(x))dx-int_(a)^(c)(f(x))dx Differentiating w.r.t. c, we get (dA)/(dc)=[2c-(a+b)]f'(c)+2f(c)+0-f(c)-(f(c)-0) For maxima and minima , (dA)/(dc)=0 rArr" "f'(c)[2c-(a+b)]=0(as f'(c)ne 0) Hence, c=(a+b)/(2) "Also for "clt(a+b)/(2),(dA)/(dc)lt0" and for "cgt(a+b)/(2),(dA)/(dc)gt0 Hence, A is minimum when c=(a+b)/(2) . If the area enclosed by f(x)= sin x + cos x, y=a between two consecutive points of extremum is minimum, then the value of a is

Indicate whether the following statements are true or false . (c) Metals can be polished.

Write T for True and F for the False. Correct the false statement The formula for calculating area is length x breadth for rectangle.

Write a value of inte^(a x)cosb x\ dx

Answer in true or false: (a+b)xx (a+c) = a+(b+c)

Write a value of int((logx)^n)/x\ dx

Write a value of int(a^x)/(3+a^x)\ dx

Write the value of int(dx)/(x^2+16)