Final answer:
To find the area bounded by the curve √x+√y=1 and the coordinate axes, we need to find the area of the quarter circle. By integrating with respect to x and evaluating the integral, we find that the area is 4/3 square units. Therefore, the correct answer is option A. 1/4 square units.
Step-by-step explanation:
The curve √x+√y=1 represents a portion of a circle. To find the area bounded by this curve and the coordinate axes, we need to find the area of the quarter circle. First, let's rewrite the equation in terms of y: y = (1 - √x)^2. Now we can find the area of the quarter circle by integrating with respect to x from 0 to 1 and then multiplying by 4.
The integral is: A = 4∫[0,1][(1 - √x)^2] dx. By simplifying the integral and evaluating it, we get: A = 4/3 square units. Therefore, the correct answer is option A. 1/4 square units.