Question

A)∫ dx=Ax+C.

b)∫xdx}=Bx∧D+C.
c)∫{(1/x∧7)dx}=Ex∧F+C.
d)∫{3x∧5dx}=Gx∧H+C.
We find that the value of A,B , F ,G, and H ( where C = integral constant.)

Answer 1

To find the values of A, B, F, G, and H in the given integrals, you apply the power rule for integration. A equals 1, B equals 1/2, F equals -6, G equals 1/6, and H equals 6.

Step-by-step explanation:

To solve for the values of A, B, F, G, and H in the integral expressions, each integral must be evaluated. Remember that C represents the constant of integration.

• For a) ∫ dx, the integral of a constant 1 with respect to x is x, so A = 1.
• For b) ∫ x dx, the integral of x with respect to x is ½ x², so B = ½.
• For c) ∫ (1/x⁷) dx, this is equivalent to ∫ x⁻⁷ dx, and the integral is -⅛ x⁻⁶, so F = -6.
• For d) ∫ 3x⁵ dx, the integral is ⅛ x⁶, which means G = ⅛ and H = 6.

These results are obtained by applying the power rule for integration, which states that the integral of x^n, where n is any real number except -1, with respect to x is ⅛ x^(n+1) + C.