let's say we have a consumer with a demand curve qd=10-p and the good it's price is 5. So the consumer will consume 5 units. The surplus of the consumer would then be equal to (10-5)+(9-5)+(8-5)+(7-5)+(6-5) = 5+4+3+2+1 = 15. However, when solving this in the conventional manner it gives me (10-5)*5/2 = 12.5
What am I doing wrong? Or is surplus just an approximation?