Write True if the statement is correct, while write false if the statement is incorrect

1. If F'(x) = f(x) for all x in an interval I, then F(x) is the antiderivative of f(x) on the interval I. 2. If ( F(x)dx = -cos.x+C then F(x) = sinx. 3. The indefinite integral of a constant & is expressed as kdxux + k. 4. The indefinite integral of the exponential function (4 dx is 4"" is + c for x -1. 5. If [ F(x)de = _+ C then F(x) = Inpod. 6. The xedx can be expressed as " du where 1 =x2. 7. The xdx can be solved by power rule of 2 antiderivative. 8. Since the expression can be written as x+1 x-1 -then dx - Into) .c. 9. If x = sin 0 , then dx is equal to cosQue . 10. The area of the shaded region in Figure 1 bounded by the curves f(x) =x2; x=3 and the x -axis can be expressed as Area = _ [ x3 dx . Figure 1 11. The definite integrals [,(7 +x2 +2x+ 1)dx and 26 (x2 + 1)dx are equal. 12. The dx is an example of improper integral. 13. The definite integral sin 3xx can be evaluated using Walli's formula. 14. The volume of the solid formed by revolving the region bounded by the graph of f(x) = x2 from x = 0to x = 3 about the y -axis (see Figure 1) is solvable by Circular Disk Method. 15. The iterated integrals jaxx ty and [ Luxury are equal