Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.

The electric current in a discharging R-C circuit is given by where R and C are constant parameters and t is time. Let i₀ = 2.00 A, R = 6.00 × 10⁵ Ω and C = 0.500 μF. (a) Find the current at t = 0.3 s. (b) Find the rate of change of current at t = 0.3 s. (c) Find approximately the current at t = 0.31 s.

Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.

Find the area bounded by the curve y = e^-x, the X-axis and the Y-axis.

A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.

A. kg/m, kg/m2

B. aL + bL²/2