Indefinite Integrals

If F(x) is a function whose derivative F'(x) = f(x) on certain interval of the x-axis, then F(x) is called the anti-derivative of indefinite integral f(x). When we integrate the differential of a function we get that function plus an arbitrary constant. In symbols we write
 

Problem 648
For the cantilever beam loaded as shown in Fig. P-648, determine the deflection at a distance x from the support.
 

Problem 647
Find the maximum value of EIδ for the beam shown in Fig. P-647.
 

Problem 646
For the beam shown in Fig. P-646, determine the value of I that will limit the maximum deflection to 0.50 in. Assume that E = 1.5 × 10⁶ psi.
 

Problem 645
Compute the deflection and slope at a section 3 m from the wall for the beam shown in Fig. P-645. Assume that E = 10 GPa and I = 30 × 10⁶ mm⁴.
 

Problem 644
Determine the maximum deflection for the beam loaded as shown in Fig. P-644.
 

Problem 643
Find the maximum value of EIδ for the cantilever beam shown in Fig. P-643.
 

Problem 642
Find the maximum deflection for the cantilever beam loaded as shown in Figure P-642 if the cross section is 50 mm wide by 150 mm high. Use E = 69 GPa.
 

Problem PG-010
The quadrilateral ABCD shown in Fig. PG-010 is inscribed in a circle with side AD coinciding with the diameter of the circle. if sides AB, BC, and CD are 8 cm, 10 cm, and 12 cm long, respectively, find the radius of the circumscribing circle.
 

Problem 641
For the cantilever beam shown in Fig. P-641, what will cause zero deflection at A?