第 12 类 RD Sharma 解 – 第 20 章定积分 – 练习 20.3 |设置 1
计算以下积分:
问题 1(i)。
解决方案:
We have,
I =
I =
Using additive property, we get
I =
I =
I = 8 + 6 – 2 – 3 + 24 + 20 – 6 – 10
I = 37
问题 1(ii)。
解决方案:
We have,
I =
I =
Using additive property, we get
I =
I =
I =
I = 0 + 1 + 3 – π/2 + e6 – e0
I = 3 – π/2 + e6
问题 1(iii)。
解决方案:
We have,
I =
I =
Using additive property, we get
I =
I =
I =
I = 63/2 + 9 – 7/2 – 3 + 64 – 36
I = 56/2 + 34
I = 62
问题2。
解决方案:
We have,
I =
We know that,
So, we get
I =
I =
I =
I = –2 + 4 – 8 – 8 + 8 + 8 – 2 + 4
I = 20
问题 3。
解决方案:
We have,
I =
We know that,
So, we get
I =
I =
I = 0 + 2 + 8 – 0
I = 10
问题 4。
解决方案:
We have,
I =
We know that,
So, we get
I =
I =
I = –1/4 + 1/2 + 1 – 1 + 1 + 1 – 1/4 + 1/2
I = 5/2
问题 5。
解决方案:
We have,
I =
We know that,
So, we get
I =
I =
I = –9/4 + 9/2 + 4 – 6 + 4 + 6 – 9/4 + 9/2
I = 25/2
问题 6。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = 1/3 – 3/2 + 2 – [8/3 – 6 + 4 – 1/3 + 3/2 – 2]
I = 1/3 – 3/2 + 2 – 8/3 + 6 – 2 + 1/3 – 3/2
I = 1
问题 7。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I = –1/6 + 1/3 – 0 + 27/2 + 3 – 1/6 – 1/3
I = 65/6
问题 8。
解决方案:
We have,
I =
We know that,
So, we get
I =
I =
I =
I = –2 + 4 + 18 – 12 + 18 + 12 – 2 + 4
I = 40
问题 9。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = -1/2 + 1 + 2 – 2 + 2 + 2 – 1/2 + 1
I = 5
问题 10。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = – 2 – 6 + 1/2 + 3
I = – 5 + 1/2
I = (-10 + 1)/2
I = -9/2
问题 11。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = 1/2 – 0 – 0 + 1/2
I = 1
问题 12。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = 1 + 1 + 1 – (–1)
I = 1 + 1 + 1 + 1
I = 4
问题 13。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = 1 – 1/√2 – 1/√2 + 1
I = 2 – 2/√2
I = 2 – √2
问题 14。
解决方案:
We have,
I =
We know that,
So we get,
I =
I =
I =
I = – 25/2 + 25 + 2 – 10 + 32 – 40 – 25/2 + 25
I = 9