Let the area bounded by the curve `y=f(x)`, x-axis and the ordinates `x=1` and `x=a` be `(a-1)sin(3a+4)`.
Statement-1: `f(x)=sin(3x+4)+3(x-1)cos(3x+4)`.
Statement-2: If `y=int_(g(x))^(h(x)) f(t)dt`, then `dy/dx=f(h(x)) h\'(x)-f(g(x)) g\'(x)`.
(A) Both 1 and 2 are true
(B) Both 1 and 2 are false
(C) 1 is true but 2 is false
(D) 1 is false but 2 is true

If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 and x=b is (b-1) sin (3b+4), then find f(x).

Statement-1: The area bounded by the curves y=x^2 and y=2/(1+x^2) is 2pi-2/3 Statement-2: The area bounded by the curves y=f(x), y=g(x) and two ordinates x=a and x=b is int_a^b[f(x)-g(x)]dx , if f(x) gt g(x) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: int_0^([x]) 4^(x-[x])dx=(3[x])/(2log2) ,Statement-2: int_0^([x]) a^(x-[x])dx=[x]int_0^1 a^(x-[x])dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area bounded by the curve y=xsinx , x-axis and ordinates x=0 and x=2pi is 4pi .Statement-2: The area bounded by the curve y=f(x) , x-axis and two ordinates x=a and x=b is int_a^b |y|dx . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Let I_1=int_0^1 e^x/(1+x)dx and I_2=int_0^1(x^2e^(x^2))/(2-x^3)dx Statement-1: I_1/I_2=3e Statement-2: int_a^b f(x)dx=int_a^b f(a+b-x)dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area bounded by the curves y=ln|x| , y-axis and y=1-|x| is 2 sq. units.Statement-2: Both the curves y=log|x| and y=1-|x| are symmetric about y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: Function f(x)=sin(x+3 sin x) is periodic . Statement-2: If g(x) is periodic then f(g(x)) periodic

Statement-1: Solution of the differential equation tany *dy/dx =sin(x+y)+sin(x-y) is secy+2cosx=c .Statement-2: The differential equation tany *dy/dx =sin(x+y)+sin(x-y) is homogenous (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area bounded by the curve y=2x^2 and y=x^2+4 is 32/3 sq. units.Statement-2: The area bounded by the curves x=f(y), x=g(y) and two abscissae y=c and y=d is int_c^d|f(y)-g(y)|dy . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area of the region R={(x,y) : |x| le |y| and x^2+y^2 le 1} is pi/4 sq. units.Statement-2: Curves |y|=|x| and x^2+y^2=1 symmetric about both x and y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true